m o korpusov a v ovchinnikov blow up of solutions of model nonlinear equations of mathematical physics



M. O. Korpusov, A. V. Ovchinnikov Blow-Up of Solutions of Model Nonlinear Equations of Mathematical Physics M. O. Korpusov, A. V. Ovchinnikov Blow-Up of Solutions of Model Nonlinear Equations of Mathematical Physics Новинка

M. O. Korpusov, A. V. Ovchinnikov Blow-Up of Solutions of Model Nonlinear Equations of Mathematical Physics

The present monography is dedicated to a fashionable trend in nonlinear analysis - the theories of blow-up of solutions for final time. In this book nonlinear Sobolev type equations are systematically studied. The book will be interesting both to experts in the field of nonlinear analysis and to students and post-graduate students of the corresponding specialties.
Periodic solutions of a certain non-linear differential equations Periodic solutions of a certain non-linear differential equations Новинка

Periodic solutions of a certain non-linear differential equations

The study of nonlinear oscillators equations is of great importance not only in all areas of physics but also in engineering and other disciplines, since most phenomena in our word are nonlinear and are described by nonlinear equations. Recently, considerable attention has been direct towards the analytical solutions for nonlinear oscillators, for example, elliptic homotopy averaging method, amplitude-frequency formulation, homotopy perturbation method, parameter-expanding method, energy balance method, and others. The aim of this thesis is to study the periodic solutions for some physical systems which the mathematical formulation of these systems leads to a certain set of nonlinear ordinary differential equations of the second order.
On Solutions of Nonlinear Functional Differential Equations On Solutions of Nonlinear Functional Differential Equations Новинка

On Solutions of Nonlinear Functional Differential Equations

Nonlinear difference equations of order greater than one are of paramount importance in applications. Such equations appear naturally as a discrete analogues and as numerical solutions of differential equations and delay differential equations. They have models in various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our goal in this thesis is understanding the dynamics of nonlinear difference equations to construct the basic theory of this ?led. We believe that the results of this thesis are prototypes towards the development of the basic theory of the global behavior of solutions of nonlinear difference equations of order greater than one. Now we are going to give some examples for applications of difference equations.
Nonlinear Diffusion For Noise Elimination Nonlinear Diffusion For Noise Elimination Новинка

Nonlinear Diffusion For Noise Elimination

A class of nonlinear diffusion equations with a power-law dependence of the coefficient on the gradient is considered. Such equations are used in the problem of suppressing image noise. The mathematical properties of this class of equations are considered. One of them ensures protection of image edges. Computational results on noise elimination in real-life images are presented. The book is intended for scientists and engineers working in mathematical physics, differential equations, and image processing and for college and university professors and postgraduate and graduate students.
Soliton Solutions Soliton Solutions Новинка

Soliton Solutions

The extended tanh method with a computerized symbolic computation, is used for constructing the travelling wave solutions of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. The applied method will be used to solve the generalized coupled Hirota Satsuma KdV equation, and seeking soliton solutions of two-component generalizations of the Kaup- Kupershmidt and Sawada-Kotera equations.
Powerful Methods for Solving Nonlinear evolution Equations Powerful Methods for Solving Nonlinear evolution Equations Новинка

Powerful Methods for Solving Nonlinear evolution Equations

It is well known that nonlinear evolution equations (NLEEs) are widely used to describe physical phenomena in various scientific and engineering fields, such as fluid mechanics, plasma physics, optical fibers, biology, solid state physics, etc. In order to understand the mechanisms of those physical phenomena, it is necessary to explore their solutions and properties. Solutions for the NLEEs can not only describe the designated problems, but also give more insights on the physical aspects of the problems in the related fields. In recent years, various powerful methods have been presented for finding exact solutions of the NLEEs in mathematical physics. The main purpose of this book is to illustrate how to establish solitary and periodic solutions of many NLEEs. Many illustrative examples are discussed by different methods, enjoy reading it.
Mathematical Tools for Hydrodynamics and Heat and Mass Transfer Mathematical Tools for Hydrodynamics and Heat and Mass Transfer Новинка

Mathematical Tools for Hydrodynamics and Heat and Mass Transfer

Modelling of processes of formation of steel ingots is carried out on the basis of solutions of multidimensional nonlinear differential equations. The process of the formation of ingots accompanied by complex turbulent processes. Therefore, this scientific papaer is devoted to describing the equations, boundary conditions, the choice of the mathematical model for the simulation of hydrodynamic processes and heat and mass transfer in the formation ingot. Much attention is paid to the software implementation and visualization of mathematical models
The analytical method solving the equations of mathematical physics The analytical method solving the equations of mathematical physics Новинка

The analytical method solving the equations of mathematical physics

The mathematical technology of the decision of linear and nonlinear regional problems is stated. On the basis of methods quasi-linearization, operational calculation and splitting on spatial variables the exact and approached analytical decisions of the equations in private derivatives of the first and second order are received. Conditions of unequivocal resolvability of a nonlinear regional problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical decisions received on offered mathematical technology, with the exact decision of regional problems and with numerical decisions on known methods are resulted. For science officers and students of older years of physical and mathematical specialists.
On Some Asymptotic Solutions of Critically Damped Nonlinear Systems On Some Asymptotic Solutions of Critically Damped Nonlinear Systems Новинка

On Some Asymptotic Solutions of Critically Damped Nonlinear Systems

The study of nonlinear problems is of crucial in the areas of Applied Mathematics, Physics and Engineering, as well as other disciplines. The differential equations are linear or nonlinear, autonomous or non-autonomous. Practically, numerous differential equations involving physical phenomena are nonlinear. Methods of solutions of linear differential equations are comparatively easy and highly developed. Whereas, very little of a general character is known about nonlinear equations. An important approach to the study of such nonlinear oscillations is the small parameter expansion of Krylov-Bogoliubov-Mitropolski (KBM). This book is concerned the critically damped nonlinear systems by use of the KBM method. The presentation of this book is easy and intelligible by the beginners. Researchers who thoroughly cover the book will be well prepared to make important contributions to analyze nonlinear systems. It will be helpful in the area of mechanics, physics, engineering etc. The book contains a wide bibliography.
Existence of Solutions of Operator Equations with Applications Existence of Solutions of Operator Equations with Applications Новинка

Existence of Solutions of Operator Equations with Applications

Various problems of a practical nature arising in physics, chemistry, biology, economy, social sciences, etc. can be modeled using a certain mathematical setup. Such models give rise to a variety of equations or a system of equations. The problems becomes more sophisticated when one deals with operator equations where the unknown object is an operator acting between two abstract spaces of different kinds. Now regarding solutions of such equations, some fundamental questions arise: Does there exist a solution? And if the answer is affirmative then it passes to the next questions: how can the solution be constructed? how many solutions are there? what is the structure of the set of all solutions? The problem of existence of a solution becomes equivalent to the problems of finding a fixed point of a certain operator. Hence results from fixed point theory can then be employed to obtain the solution of an operator equation. Banach's contraction principle is broadly applicable in proving the existence of solutions to operator equations, including ordinary differential equations, partial differential equations and integral equations. This principle has been generalized in many directions.
Qualitative Studies of Scalars and Systems of Difference Equations Qualitative Studies of Scalars and Systems of Difference Equations Новинка

Qualitative Studies of Scalars and Systems of Difference Equations

The authors interested in studying the qualitative behavior (such as : local stability – global stability – periodic nature – boundedness – semi cycles analysis – oscillation – how to find the analytical forms of the solutions, etc... ) for some nonlinear difference equations and systems of difference equations as well as provide and structure mathematical models in various fields of life.
Applications of Symmetries for Solutions of Einstein Equations Applications of Symmetries for Solutions of Einstein Equations Новинка

Applications of Symmetries for Solutions of Einstein Equations

General relativity is a physical theory which nowadays plays a key role in astrophysics and in physics and in this way it is important for a number of ambitious experiments and space missions. Einstein equations are central piece of general relativity. Einstein equations are expressed in terms of coupled system of highly nonlinear partial differential equations describing the matter content of space-time. The present work is to give an exposition of parts of the theory of partial differential equations that are needed in this subject and to represent exact solutions to Einstein equations. This book deals with various system of non linear partial differential equations corresponding to the Einstein equations for non diagonal Einstein-Rosen Metrics, Cylindrically Symmetric Null Fields, Vacuum Field Equations etc. from the view point of underlying symmetries and then to obtain their some new explicit exact solutions by using symmetry techniques like Lie symmetry analysis, symmetry reduction etc. These exact solutions play a significant for understanding of various phenomenons and are utilized for checking validity of numerical and approximation techniques and programs.
Nonlinear Fractional Order Differential Equations Nonlinear Fractional Order Differential Equations Новинка

Nonlinear Fractional Order Differential Equations

The main purpose of this work is to study the fractional order linear and nonlinear differential equations. This book is to present the analytical solutions of fractional order differential equations. The book is divided into two main parts: (a) - The fractional order ordinary and (b) - The fractional order partial differential equations. The aim of presenting, in a systematic manner, results including the solutions of linear and nonlinear system of fractional order equations arising in chemical kinetics by homotopy and variational methods, fractional order Riccati differential equations by less computational homotopy approach, explicit solutions of linear and nonlinear system of fractional order differential equations, nonlinear fractional order Swift–Hohenberg (S-H) equation, the fractional order Burgers equations and the time-fractional reaction-diffusion equations. The non-perturbative and numerical methods have been implemented to obtain the solutions of considered problems. Results will be developed which are useful for the researchers and it is also useful which will interact to its practical applications with engineers and mathematician.
Improved Tanh and Sech Methods for Obtaining New Exact Solutions Improved Tanh and Sech Methods for Obtaining New Exact Solutions Новинка

Improved Tanh and Sech Methods for Obtaining New Exact Solutions

Exact solutions to nonlinear evolution equations (NEEs) play an important role in nonlinear physical science, since the characteristics of these solutions may well simulate real-life physical phenomena. One of the benefits of finding new exact solutions to such nonlinear partial differential equations (PDEs) is to give a better understanding on the various characteristics of the solutions. The main task of this work is to show that our proposed methods, improved tanh and sech methods, are very efficient in solving various types of NEEs and PDEs including special equations than using classical tanh and sech methods. This efficiency is because of their rich with the multiple traveling wave solutions than classical tanh and sech methods. From the obtained results, we can not only recover the previous solutions obtained by some authors but also obtain some new and more general solitary wave, singular solitary wave and periodic solutions. Illustrating the theory of nonlinear transmission lines (NLTLs), showing the ability of NLTL to generate solitons and solving the model equation of NLTL in presence of loss are other tasks of this book.
Geometry of Partial Differential Equations Geometry of Partial Differential Equations Новинка

Geometry of Partial Differential Equations

The study of partial differential equations has been the object of much investigation and seen a great many advances recently. This is primarily due to the fact that certain classes of these equations fall under the category of being integrable. These kinds of equations have many useful properties such as the existence of Lax pairs, Backlund transformations, explicit solutions and the existence of a correspondence with geometric manifolds. There have also been many applications of solutions to these equations in the study of solitons and other objects which have seen applications in physics. It is the objective here to study some of these equations in a general way by using various ideas that have evolved in the evolution of the subject of differential geometry. The first sections give some introductory material related to the subject, and then the latter sections seek to apply these ideas to obtain many useful results with regard to nonlinear equations and to some examples of nonlinear equations in particular. Each chapter is self-contained and can be read on its own if desired.
Singular Initial Value Problems Singular Initial Value Problems Новинка

Singular Initial Value Problems

The aim of this book is to use a semi-analytic technique for solving singular initial value problems of ordinary differential equations with a singularity of different kinds to construct polynomial solution using two point osculatory interpolation. The efficiency and accuracy of suggested method is assessed by comparisons with exact and other approximate solutions for a wide classes of non–homogeneous,non–linear singular initial value problems. Many examples are presented to demonstrate the applicability and efficiency of the suggested method on one hand and to confirm the convergence order on the other hand,two applications in mathematical physics and astrophysics are presented,such as Lane–Emden equations and Emden–Fowler equations to model several problems such as the theory of stellar structure,the thermal behavior of a spherical cloud of gas, isothermal gas spheres and the theory of thermionic currents.
Solutions of Nonlinear Parabolic Differential Equations Solutions of Nonlinear Parabolic Differential Equations Новинка

Solutions of Nonlinear Parabolic Differential Equations

In this book, solutions of nonlinear parabolic differential equations are investigated. More specifically, existence and non-existence theorems of solutions are presented. The first part involves the related results for the Cauchy problem for a set of nonlinear parabolic differential equations with critical exponent. Then the necessary and sufficient conditions are determined for the non-existence results of solutions for the corresponding Dirichlet and mixed boundary value problems. The proofs make use of the dilation and comparison arguments. Moreover, to generalize these results, proofs are given in n-dimension and for general type of domains. Finally, numerical simulations are also provided to verify the theoretical analysis
Existence and stability of solutions to nonlinear dynamical systems Existence and stability of solutions to nonlinear dynamical systems Новинка

Existence and stability of solutions to nonlinear dynamical systems

This book is an outgrowth of our results on the existence and stability of solutions to nonlinear dynamical systems, stochastic systems, and impulsive systems over the last five years. In particular, we present the Razumikhin-type exponential stability criteria for impulsive stochastic functional differential systems, the stability analysis of neutral stochastic delay differential equations by a generalization of Banachs contraction principle and the globally asymptotical stability in the mean square for stochastic neural networks with time-varying delays and fixed moments of impulsive effect. Also, we discuss oscillation criteria based on a new weighted function for linear matrix Hamiltonian systems and the existences of the positive solutions or nontrivial solutions of nonlinear differential equations.
Numerical Solutions of Algebraic, Differential and Integral Equations Numerical Solutions of Algebraic, Differential and Integral Equations Новинка

Numerical Solutions of Algebraic, Differential and Integral Equations

Designed for advanced undergraduate and graduate students in applied mathematics as well as researchers, this illuminating resource will introduce the reader to the fundamental aspects of three powerful iterative methods for handling equations with distinct structures. The book will serve nicely as a supplementary textbook for course study. The aim of this textbook is threefold: firstly, give a detailed review of the Adomian Decomposition Method for solving linear/nonlinear ordinary and partial differential equations, algebraic equations, delay differential equations, linear and nonlinear integral equations, and integro-differential equations. Secondly, the essential features of the He’s Variational Iteration Method are rigorously presented for solving a wide spectrum of equations. Finally, introduce a novel method based on manipulating Green’s functions and some popular fixed point iterations schemes, such as Picard's and Mann's, for the numerical solution of boundary value problems.
J. Oden Tinsley An Introduction to Mathematical Modeling. A Course in Mechanics J. Oden Tinsley An Introduction to Mathematical Modeling. A Course in Mechanics Новинка

J. Oden Tinsley An Introduction to Mathematical Modeling. A Course in Mechanics

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.
A Method for Solve the Nonlinear Fractional Differential Equations A Method for Solve the Nonlinear Fractional Differential Equations Новинка

A Method for Solve the Nonlinear Fractional Differential Equations

In this book is presented a new method introduced in order to establish solutions for fractional differential equations. This method is based on a combination of Adomian decomposition method and Laplace transform method. This new method can be applied to linear and nonlinear fractional differential equations. The method is illustrated on a series of examples including ordinary differential equations and systems of differential equations, partial differential equations and systems. The method can be used with the aid of symbolic calculus. For this reason we are suggested some Maple and Mathematica solutions of the examples investigated.
Monte Carlo method for linear and nonlinear boundary value problems Monte Carlo method for linear and nonlinear boundary value problems Новинка

Monte Carlo method for linear and nonlinear boundary value problems

Availability of multiprocessor computers, allows us to solve many complex problems using Monte Carlo method. Monte Carlo methods have been further developed to solve a variety of multidimensional integrals, linear and nonlinear boundary value problems. In monograph we used the deep connections between differential equations and random processes. This connection has been known long ago, the results of the theory of differential equations have been widely used in the theory of probability and vice versa. The solutions of large class linear and nonlinear equations of elliptic and parabolic type may be represented in the form of integrals over the trajectories of Markov process. In the current work we study the approaches connected with simple and branching Markov processes. We obtained effective unbiased estimators for the solutions. Constructed numerical algorithms are strict proved and used for the solution of problems of mathematical physics. This book meant for specialists of numerical methods who applied Monte Carlo methods for the solution boundary value problems, calculating multidimensional integrals and work in the area financial mathematics and statistics.
Integral Equations and Integro-Partial Differential Equations Integral Equations and Integro-Partial Differential Equations Новинка

Integral Equations and Integro-Partial Differential Equations

The theory of integral equations has a close contact with many different areas of mathematics. This is sufficient to say that there is almost no area of applied sciences and physics where integral equations do not play an important role. This books intended primarily to study the existence of solution , analytically and numerically, of nonlinear integral equations of the second kind of types Hammerstein, Hammerstein- Volterra and Volterra-Hammerstein. Also, it is used for proving the existence and uniqueness solution, analytically, of linear integro-differential and integral equations of type Fredholm-Volterra in three dimensional. Finally, it is very useful in establishing the existence and uniqueness solution of linear and nonlinear partial differential equations of fractional order, analytically and numerically.
Evolution Equations and Applications Evolution Equations and Applications Новинка

Evolution Equations and Applications

In this book, we present the fundamental theory of abstract Evolution Equations by using the semigroup approach. More precisely, first we review the basic notions of Functional Analysis and Differential Analysis, secondly we study the theory of semigroups of bounded linear operators, and thirdly we consider Linear Evolution Equations and moreover we give existence results for Semilinear Evolution Equations of the form: du/dt= Au + f(t; u); t 0 ; u(0) = u_0 where A is a linear operator that is the infinitesimal generator of a C_0-semigroup of bounded linear operators on a Banach space and f satisfies certain Lipschitz, and Linear growth conditions. As applications we show the existence of solutions to some Homogeneous Heat Equations, classical Wave equations, nonlinear Heat Equation, and to some nonlinear Wave equation.
Computer-assisted enclosures for fourth order elliptic equations Computer-assisted enclosures for fourth order elliptic equations Новинка

Computer-assisted enclosures for fourth order elliptic equations

"Concerning (partial) differential equations, amongst many others two questions are of great importance: existence and uniqueness, or more general multiplicity of solutions... There are plenty of equations, where analytical methods fail to work." The author describes in this work a computer-assisted method for proving existence and multiplicity of solutions of fourth order nonlinear elliptic boundary value problems. The main idea of this method is to compute a good numerical approximation of a solution and certain defect bounds with computer-assistance. Then a rigorous proof of the existence of an exact solution close to the numerical one is obtained by a fixed-point argument. The efficiency of this method is demonstrated with the examples of the fourth order Gelfand- and Emden-equations on various domains.
Applications of Lie Group to Some Nonlinear Equations Applications of Lie Group to Some Nonlinear Equations Новинка

Applications of Lie Group to Some Nonlinear Equations

Keeping in view the rich treasure and wide applicability of nonlinear equations in almost every field, we have in this book carried out the application of Lie group analysis for obtaining exact solutions to nonlinear partial differential equations. In particular, this book is devoted to a wide range of applications of continuous symmetry groups to two physically important systems i.e. the (2+1)-dimensional Calogero Degasperis equation with its variable coefficients form and the (2+1)-dimensional potential Kadomstev Petviashvili equation along its generalized form. In recent years, much attention has also been paid to equations with variable coefficients as the physical situations in which nonlinear systems arise tend to be highly idealized due to assumption of constant coefficients. This has led us to undertake the study of equations with variable coefficients and to derive the admissible forms of the coefficients along with their exact solutions. The efforts are thus concentrated on finding the symmetries, reductions and exact solutions of certain nonlinear equations by using various methods.
On a Study of Some Difference Equations including Bifurcation Analysis On a Study of Some Difference Equations including Bifurcation Analysis Новинка

On a Study of Some Difference Equations including Bifurcation Analysis

We consider some recurrence relations, which has been investigated earlier by M. Qena. We extend some of the results regarding the existence of periodic solutions. Furthermore, we try to study the behavior of the solutions in other cases. We were able to show the unboundedness and specifically the monotone increasing behavior in many of these cases. We then started a bifurcation analysis for the behavior of the solutions, by which we used the computer in order to do some calculations without any rigorous mathematical proofs.
Lie-group analysis of Newtonian/non-Newtonian fluids flow Lie-group analysis of Newtonian/non-Newtonian fluids flow Новинка

Lie-group analysis of Newtonian/non-Newtonian fluids flow

In this book, group methods are presented for finding the similarity solutions for some systems of partial differential equations, which govern the problems of convective flow in the boundary layer of Newtonian and non-Newtonian fluid. We will use three methods for finding the similarity representations (i) Scaling transformations, (ii) Infinitesimal Lie group analysis and (iii) Suitable similarity transformations. Lie groups, and hence their infinitesimal generators, can be naturally extended or "prolonged" to act on the space of independent variables, dependent variables and derivatives of the dependent variables up to any finite order. As a consequence, the seemingly intractable nonlinear conditions of group invariance of a given system of differential equations reduce to linear homogeneous equations determining the infinitesimal generators of the group. Since these determining equations form an over determined system of linear homogeneous partial differential equations. If a system of partial differential equations is invariant under a Lie group of point transformations, one can find, constructively, special solutions, called similarity solutions or invariant solutions.
William Schiesser E. Differential Equation Analysis in Biomedical Science and Engineering. Ordinary Differential Equation Applications with R William Schiesser E. Differential Equation Analysis in Biomedical Science and Engineering. Ordinary Differential Equation Applications with R Новинка

William Schiesser E. Differential Equation Analysis in Biomedical Science and Engineering. Ordinary Differential Equation Applications with R

Features a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fields With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-world ODE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear ordinary differential equations. The author’s primary focus is on models expressed as systems of ODEs, which generally result by neglecting spatial effects so that the ODE dependent variables are uniform in space. Therefore, time is the independent variable in most applications of ODE systems. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for ODEs Models as systems of ODEs with explanations of the associated chemistry, physics, biology, and physiology as well as the algebraic equations used to calculate intermediate variables Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general ODE computation through various biomolecular science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.
Symmetries and Exact Solutions for Nonlinear Systems Symmetries and Exact Solutions for Nonlinear Systems Новинка

Symmetries and Exact Solutions for Nonlinear Systems

The importance of the nonlinear systems due to their common occurrence in the study of physical phenomena and also the various limitations posed by the linear systems theory have been the prime reasons for the studies of nonlinear models as such. The physical situations in which nonlinear equations arise tend to be highly idealized with the assumption of constant coefficients. Due to this, much attention has been paid on study of nonlinear equations with variable coefficients. This book deals with nonlinear partial differential equations with variable coefficients representing some interesting physical systems viz. coupled KdV system, generalized Hirota-Satsuma KdV, variant Boussinesq, modified Boussinesq and a family of non-evolution equations, from the view point of their underlying Lie point symmetries and to obtain their exact solutions. Since the nonlinear systems with variable coefficients are very difficult to handle, hence this book shall provide freedom for the researchers to obtain the symmetries and exact solutions for variable coefficients nonlinear systems and further to simulate the desired physical situations.
Introduction to Atmospheric Physics for Under graduate students Introduction to Atmospheric Physics for Under graduate students Новинка

Introduction to Atmospheric Physics for Under graduate students

Atmospheric physics is the application of physics to the study of the atmosphere surrounding the Earth.physicists attempt to model Earth's atmosphere and the atmospheres of the other planets using fluid flow equations, chemical models, radiation budget, and energy transfer processes in the atmosphere (as well as how these tie into other systems such as the oceans). In order to model weather systems, atmospheric physicists employ elements of scattering theory, wave propagation models, cloud physics, statistical mechanics and spatial statistics which are highly mathematical and related to physics.
Willatzen Morten Separable Boundary-Value Problems in Physics Willatzen Morten Separable Boundary-Value Problems in Physics Новинка

Willatzen Morten Separable Boundary-Value Problems in Physics

Innovative developments in science and technology require a thorough knowledge of applied mathematics, particularly in the field of differential equations and special functions. These are relevant in modeling and computing applications of electromagnetic theory and quantum theory, e.g. in photonics and nanotechnology. The problem of solving partial differential equations remains an important topic that is taught at both the undergraduate and graduate level. Separable Boundary-Value Problems in Physics is an accessible and comprehensive treatment of partial differential equations in mathematical physics in a variety of coordinate systems and geometry and their solutions, including a differential geometric formulation, using the method of separation of variables. With problems and modern examples from the fields of nano-technology and other areas of physics. The fluency of the text and the high quality of graphics make the topic easy accessible. The organization of the content by coordinate systems rather than by equation types is unique and offers an easy access. The authors consider recent research results which have led to a much increased pedagogical understanding of not just this topic but of many other related topics in mathematical physics, and which like the explicit discussion on differential geometry shows – yet have not been treated in the older texts. To the benefit of the reader, a summary presents a convenient overview on all special functions covered. Homework problems are included as well as numerical algorithms for computing special functions. Thus this book can serve as a reference text for advanced undergraduate students, as a textbook for graduate level courses, and as a self-study book and reference manual for physicists, theoretically oriented engineers and traditional mathematicians.
On Some Iterative Methods for Solving System of Nonlinear Equations On Some Iterative Methods for Solving System of Nonlinear Equations Новинка

On Some Iterative Methods for Solving System of Nonlinear Equations

Various problems of pure and applied sciences such as physics, chemistry, biology, engineering, economics, management sciences, industrial research and optimization can be studied in the unified frame work of the system of nonlinear equations. In this study, we develop several new iterative methods for solving a system of nonlinear equations by using different techniques, including quadrature technique, new decomposition method and variational iteration technique. We prove the convergence of the new methods. We obtain the upper bounds of the error of new methods. We also discuss the efficiency index of the proposed methods and compare it with some other well-known methods. We provide several examples for the implementation and performance of the new methods. Comparison with some other existing methods is also given. We also discuss some open research problems.
Modifications of homotopy perturbation & variational iteration methods Modifications of homotopy perturbation & variational iteration methods Новинка

Modifications of homotopy perturbation & variational iteration methods

Solutions of the mathematical models well simulate real-life physical behavior of the physical problems. So, and with the development of computer algebraic systems, many analytical and numerical techniques for obtaining the target solutions have taken a lot of interest. The book includes a detailed investigation of two recently developed analytical methods that show potential in solving nonlinear equations of various kinds (differential, integral, integro-differential, difference-differential) without discretizing the equations or approximating the operators. The considered methods are mainly the homotopy perturbation method (HPM) and the variational iteration method (VIM). In this work, basic ideas of the HPM and VIM are illustrated; convergence theorems of the considered methods for various types of equations are proved; modifications and treatments in HPM and VIM are done; test examples for further illustration of the methods are solved; many applications in fluid mechanics and physics fields are investigated using modified techniques; and finally, all obtained results are verified through the comparison with exact/numerical solutions or previously published results.
Contribution to the Study of a Mathematical Model of Erythropoiesis Contribution to the Study of a Mathematical Model of Erythropoiesis Новинка

Contribution to the Study of a Mathematical Model of Erythropoiesis

The asymptotic stability of a nonlinear system of three differential equations with delay is analyzed, describing the dynamics of red blood cell production. This process is based on the differentiation of stem cells, throughout divisions, into mature blood cells, that in turn control the dynamics of immature cells. Taking into account an explicit role of the mature cell population on the cell proliferation, a characteristic equation with delay dependent coefficients is studied. A necessary and sufficient condition for stability of the zero fixed point is determined. Finally, the existence of a Hopf bifurcation for the only positive fixed point is obtained, leading to the existence of periodic solutions.
Mathematical study of eco-epidemiological system Mathematical study of eco-epidemiological system Новинка

Mathematical study of eco-epidemiological system

Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations. These and other types of models can overlap, with a given model involving a variety of abstract structures. In general, mathematical models may include logical models. One of these models the effect of diseases in ecological system Which is an important issue from mathematical and experimental point of view. Such models are called eco-epidemiological models. Eco-epidemiological model is comparatively a new branch in mathematical biology which simultaneously considers the ecological and epidemiological processes.
Analysis of the SDE/Monte Carlo Approach in Studying Nonlinear Systems Analysis of the SDE/Monte Carlo Approach in Studying Nonlinear Systems Новинка

Analysis of the SDE/Monte Carlo Approach in Studying Nonlinear Systems

The reader is about to embark on a tutorial journey through a series of nonlinear dynamic systems that contain a rich tapestry of phenomena and solutions. The study of nonlinear systems can be greatly enhanced by the combined use of the stochastic dynamic equations and Monte Carlo calculations. When a dynamic system is forced and dissipative all the trajectories tend toward a bounded set of zero volume - often a strange attractor with a fractal dimension. The stochastic dynamic equations can directly reveal the statistical moments of the system, but their direct solution is inefficient, and they are not a closed set. The power of the combined method is that the time averaged Monte Carlo moments will agree exactly with equations described by the left hand side of the full stochastic dynamic equations set to zero - no closure is required. Every equation expresses an exact relationship among the variables. One is able to delve far deeper into the nature of the nonlinear systems. This tutorial exposition offers the tools for the past nonlinear modeling efforts in the traditional physical sciences and in various complex modeling problems in new fields of biology and health sciences.
Eurhythmic Physics or Hyperphysics Eurhythmic Physics or Hyperphysics Новинка

Eurhythmic Physics or Hyperphysics

Eurhythmic Physics is a global approach allowing the unification of physics. Assumes that natural physical phenomena are very complex and that, in general, the whole is different from the sum of the constituent parts. So, to be best described, need a complex inter-relational nonlinear approach. The mathematical formulation of this complex inter-relational and nonlinear physics is mainly done through the organizing principle of Eurhythmy. Eurhythmic Physics leads to a deeper understanding of the physical reality. In such conditions, classical physics, relativity and quantum physics are susceptible of a unique unitary and causal description. Furthermore, allows a deeper understanding of what is commonly called gravitation, gravitic interaction, the concept of mass, and the electromagnetic phenomena. The complex inter-relational nonlinear approach furnishes also the basis for understanding what lies behind the invariance of the velocity of the light in the most common circumstances. The apparent mystery behind quantum tunneling and zero-time transitions is easily clarified when we look at it with the eyes of the New Physics.
Vibration Control Of A Nonlinear Magnetic Levitation System Vibration Control Of A Nonlinear Magnetic Levitation System Новинка

Vibration Control Of A Nonlinear Magnetic Levitation System

The main objective of this book is a mathematical study for mechanical vibrations of a magnetic levitation system described by a nonlinear ordinary differential equation. It is being suggested some forms of active conventional control techniques to suppress such vibrations, then applying the multiple scales perturbation method to solve these nonlinear differential equations approximately. The corresponding frequency-response equations are extracted and plotted at the different system parameters. The obtained graphs are confirmed numerically applying Rung-Kutta algorithm of fourth order. The concluded results are summarized and a comparison of the different control methods is presented. Finally, a list of references is cited.
Eric Chin Problems and Solutions in Mathematical Finance. Equity Derivatives, Volume 2 Eric Chin Problems and Solutions in Mathematical Finance. Equity Derivatives, Volume 2 Новинка

Eric Chin Problems and Solutions in Mathematical Finance. Equity Derivatives, Volume 2

Detailed guidance on the mathematics behind equity derivatives Problems and Solutions in Mathematical Finance Volume II is an innovative reference for quantitative practitioners and students, providing guidance through a range of mathematical problems encountered in the finance industry. This volume focuses solely on equity derivatives problems, beginning with basic problems in derivatives securities before moving on to more advanced applications, including the construction of volatility surfaces to price exotic options. By providing a methodology for solving theoretical and practical problems, whilst explaining the limitations of financial models, this book helps readers to develop the skills they need to advance their careers. The text covers a wide range of derivatives pricing, such as European, American, Asian, Barrier and other exotic options. Extensive appendices provide a summary of important formulae from calculus, theory of probability, and differential equations, for the convenience of readers. As Volume II of the four-volume Problems and Solutions in Mathematical Finance series, this book provides clear explanation of the mathematics behind equity derivatives, in order to help readers gain a deeper understanding of their mechanics and a firmer grasp of the calculations. Review the fundamentals of equity derivatives Work through problems from basic securities to advanced exotics pricing Examine numerical methods and detailed derivations of closed-form solutions Utilise formulae for probability, differential equations, and more Mathematical finance relies on mathematical models, numerical methods, computational algorithms and simulations to make trading, hedging, and investment decisions. For the practitioners and graduate students of quantitative finance, Problems and Solutions in Mathematical Finance Volume II provides essential guidance principally towards the subject of equity derivatives.
The Dynamics of Prey-Predator Systems with A Prey Refuge The Dynamics of Prey-Predator Systems with A Prey Refuge Новинка

The Dynamics of Prey-Predator Systems with A Prey Refuge

In this work , A stability analysis of an eco-epidemiological model incorporating prey refuge is investigated . Two types of prey- predator models with disease in a prey incorporating prey refuge are proposed and analyzed Both models are represented mathematically by system of nonlinear differential equations. The existence, uniqueness and boundedness of the solutions of these two models and the permanence are investigated. The local and global stability conditions of all possible equilibrium points are established. Finally, numerical simulation is used to study the global dynamics of both models.
Applications of The Summation and Recurrence Equations Applications of The Summation and Recurrence Equations Новинка

Applications of The Summation and Recurrence Equations

The monograph presented shows new models of mathematical uniform difference operators and their applications for the analytical sum determination of infinite series. Various properties of the uniform difference operator and its inverse form are presented here. The domain of the uniform difference operator is the discrete number space. The monograph takes the further application steps of the uniform difference operator and presents the general and particular solutions of n-order difference and recurrence linear homogeneous and non-homogeneous ordinary and partial equations with constant and variable coefficients. The monograph presents numerous calculations and solutions of the examples of choices. In this monograph the mathematical and numerical achievements are presented and discussed especially solutions of summation and recurrence equations, applied in the computational mechanics computer science and control systems.
Albert C. J. Luo Analytical Routes to Chaos in Nonlinear Engineering Albert C. J. Luo Analytical Routes to Chaos in Nonlinear Engineering Новинка

Albert C. J. Luo Analytical Routes to Chaos in Nonlinear Engineering

Nonlinear problems are of interest to engineers, physicists and mathematicians and many other scientists because most systems are inherently nonlinear in nature. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations. This works well up to some accuracy and some range for the input values, but some interesting phenomena such as chaos and singularities are hidden by linearization and perturbation analysis. It follows that some aspects of the behavior of a nonlinear system appear commonly to be chaotic, unpredictable or counterintuitive. Although such a chaotic behavior may resemble a random behavior, it is absolutely deterministic. Analytical Routes to Chaos in Nonlinear Engineering discusses analytical solutions of periodic motions to chaos or quasi-periodic motions in nonlinear dynamical systems in engineering and considers engineering applications, design, and control. It systematically discusses complex nonlinear phenomena in engineering nonlinear systems, including the periodically forced Duffing oscillator, nonlinear self-excited systems, nonlinear parametric systems and nonlinear rotor systems. Nonlinear models used in engineering are also presented and a brief history of the topic is provided. Key features: Considers engineering applications, design and control Presents analytical techniques to show how to find the periodic motions to chaos in nonlinear dynamical systems Systematically discusses complex nonlinear phenomena in engineering nonlinear systems Presents extensively used nonlinear models in engineering Analytical Routes to Chaos in Nonlinear Engineering is a practical reference for researchers and practitioners across engineering, mathematics and physics disciplines, and is also a useful source of information for graduate and senior undergraduate students in these areas.
Kopylova Elena Dispersion Decay and Scattering Theory Kopylova Elena Dispersion Decay and Scattering Theory Новинка

Kopylova Elena Dispersion Decay and Scattering Theory

A simplified, yet rigorous treatment of scattering theory methods and their applications Dispersion Decay and Scattering Theory provides thorough, easy-to-understand guidance on the application of scattering theory methods to modern problems in mathematics, quantum physics, and mathematical physics. Introducing spectral methods with applications to dispersion time-decay and scattering theory, this book presents, for the first time, the Agmon-Jensen-Kato spectral theory for the Schr?dinger equation, extending the theory to the Klein-Gordon equation. The dispersion decay plays a crucial role in the modern application to asymptotic stability of solitons of nonlinear Schr?dinger and Klein-Gordon equations. The authors clearly explain the fundamental concepts and formulas of the Schr?dinger operators, discuss the basic properties of the Schr?dinger equation, and offer in-depth coverage of Agmon-Jensen-Kato theory of the dispersion decay in the weighted Sobolev norms. The book also details the application of dispersion decay to scattering and spectral theories, the scattering cross section, and the weighted energy decay for 3D Klein-Gordon and wave equations. Complete streamlined proofs for key areas of the Agmon-Jensen-Kato approach, such as the high-energy decay of the resolvent and the limiting absorption principle are also included. Dispersion Decay and Scattering Theory is a suitable book for courses on scattering theory, partial differential equations, and functional analysis at the graduate level. The book also serves as an excellent resource for researchers, professionals, and academics in the fields of mathematics, mathematical physics, and quantum physics who would like to better understand scattering theory and partial differential equations and gain problem-solving skills in diverse areas, from high-energy physics to wave propagation and hydrodynamics.
Nonlinear Mathematical Modeling in Atmosphere and Ocean Nonlinear Mathematical Modeling in Atmosphere and Ocean Новинка

Nonlinear Mathematical Modeling in Atmosphere and Ocean

The purpose of this monograph is to provide illustrative examples of nonlinear modeling of oceanic and atmospheric dynamics and associated energetic. Particularly,exact solutions for the Navier-Stokes equations and the corresponding energy balance associated with an atmospheric motion around the Earth are presented. Additionally,nonlinear internal gravity waves forming a column of stratified fluid affected by the Earth's rotation are considered. In terms of linear modeling,the energy density was visualized as spinning patterns that appear to be rotating in an anticlockwise sense. Such spinning patterns were compared with the flow around a low-pressure area that is usually being linked with a modeling of hurricanes. In terms of nonlinear analysis,several classes of exact solutions were found.One particular class was visualized as funnels having something in common with the geometric structure of oceanic whirlpools. Up to the present,it remains an open issue where the whirlpools came from and what surprises they may bring to. However,it is recognized that the oceanic whirlpools play a key role in global climate. Additionally,such whirlpools show influence on the atmosphere.
Theory of Nonlinear Synthesis of Radiating Systems Theory of Nonlinear Synthesis of Radiating Systems Новинка

Theory of Nonlinear Synthesis of Radiating Systems

In this book are presented the theory and methods for solving nonlinear synthesis problems of various types of radiating systems arising during optimal design. Variational formulations of problems, in which are given only requirements to amplitude directivity pattern (DP) or DP by power, and to amplitude and phase (amplitude or phase) of distribution of excitation sources of electromagnetic fields, are given. Characteristic feature of these classes of problems is nonuniqueness and branching (or bifurcation) of existing solutions. Research and finding of optimal solutions of the synthesis problems is reduced to the study and numerical solution of nonlinear integral equations of Hammerstein type. There are given the numerical methods to solving the synthesis problems of such radiating systems: linear antennas, antenna with flat aperture, linear and planar antenna arrays (AA), microstrip arrays, adaptive AA, hybrid reflector and lens antennas and synthesis on the basis of contour DPs of fixed and variable form. This book can be used by the experts in the antennas theory, applied mathematics and mathematical physics, by students and post-graduate students of corresponding specialties.
Discrete Symmetries for the higher dimensional heat equation Discrete Symmetries for the higher dimensional heat equation Новинка

Discrete Symmetries for the higher dimensional heat equation

Difference equations are very useful in daily life. There are lot of applications of difference equations in business, statistics, economics, computer programming and numerical solutions of differential equations. In mathematics, there are two reasons for using the difference equations. Firstly, difference equations play an important role in the designing of mathematical models which are used in mechanics and mathematical physics. Such kind of models relay on symmetries. The existence of exact analytical solution of the difference equation and their conservation laws are related to their continuous symmetries. Secondly, in the theory of differential equation (D.E), system of D.E. can be replaced by using difference equations and meshes. In this book, a complete symmetry analysis for the multidimensional discrete heat equation is presented. For this, generalized prolongations are reported for the considered equation. Furthermore, Lie point generators are computed for n=2, 3 and then generalized for the arbitrary value of n. A relationship between the number of the symmetries and the value of n is given at last.
Exact Solutions of Evolution Equations with Variable Coefficients Exact Solutions of Evolution Equations with Variable Coefficients Новинка

Exact Solutions of Evolution Equations with Variable Coefficients

In this book, we make an extension to the unified method that unifies all the known methods in the literature for finding the exact solutions of scalar or vector nonlinear PDE's with constant coefficients in the nonlinear sciences. The extended unified method unable us to investigate the effects of the inhomogeneity of the diffusion, diffraction dispersion super-diffusion of the medium trough considering the coefficients space-dependent. On the other hand, some problems have been studied when these coefficients are taken as time-dependent. The main objectives of the extended unified method are; (a) Constructing the necessary conditions for the existence of solutions to evolution equations. (b) Whenever the solutions exist, this method suggests a new classification to the solution structures namely; the polynomial solutions, the rational solutions and the polynomial-rational solutions. In each type, we mean that the obtained equations are accomplished by a set of auxiliary equation whose solution gives rise to an auxiliary function.
Equivariant Degree with Symmetric Nonlinear Boundary Value Problems Equivariant Degree with Symmetric Nonlinear Boundary Value Problems Новинка

Equivariant Degree with Symmetric Nonlinear Boundary Value Problems

The Boundary value/periodic problems for the nonlinear equation (or, more generally, second order nonlinear ODEs) have been the focus of nonlinear analysis study for a long time. The goal of this book is to show how the equivariant degree theory can be used for the systematic study of multiple solutions to several (symmetric) generalizations of BVP and for the classification of symmetric properties of these solutions. There are several classical methods of nonlinear analysis used to solve the BVP. However, their application encounters serious difficulties if: the group of symmetries is large, the dimension of the problem is high, and multiplicities of eigenvalues of linearizations are large, etc. In this book, we: (i) set up the abstract functional analysis framework for studying symmetric properties of multiple solutions to symmetric generalizations of the BV problem via the equivariant degree approach; (ii) describe wide classes of second order BVPs admitting dihedral symmetries to which the abstract theory can be effectively applied; (iii) and apply the obtained results to several classes of implicit second order symmetric differential equations.
Variational Iteration Method Variational Iteration Method Новинка

Variational Iteration Method

Differential equations are encountered in various fields such as physics, chemistry, biology, mathematics and engineering. Most nonlinear models of real-life problems are still very difficult to solve either numerically or theoretically. Many unrealistic assumptions have to be made to make nonlinear models solvable. There has recently been much attention devoted to the search for better and more efficient solution methods for determining a solution, approximate or exact, analytical or numerical, to nonlinear models. Finding exact/approximate solutions of these nonlinear equations are interesting and important. One of these methods is variational iteration method (VIM), which has been proposed by Ji-Huan He in 1997 based on the general Lagrange’s multiplier method. The main feature of the method is that the solution of the linearized problem is used as the initial approximation for the linear and nonlinear problems. Then a more highly precise approximation at some special point can be obtained. This approximation converges rapidly to an accurate solution. VIM is very powerful and efficient in finding analytical as well as numerical solutions for a wide class of differential equation
Methods of Studies of Integro-Differential Equations with Parameters Methods of Studies of Integro-Differential Equations with Parameters Новинка

Methods of Studies of Integro-Differential Equations with Parameters

We consider the questions of development and substantiation of the reduction of a boundary-value problem for linear and weakly nonlinear integro-dierential equations with parameters and restrictions to an equivalent integral equation without restrictions. The applications of the iterative, projective, and projective-iterative methods to the boundary-value problems for linear integro-dierential equations with parameters and restrictions are studied and justied. Some computational algorithms of the projective-iterative and modied projective-iterative methods for weakly nonlinear integro-dierential equations with parameters and restrictions are proposed.
Functional equations and characterization problems Functional equations and characterization problems Новинка

Functional equations and characterization problems

Solution of functional equations is an old problem of mathematical analysis. Functional equations and their applications are widely studied and can be applied in economics, physics and statistics as well. The results of the book are partly connected to the investigation of functional equations with restricted domains, for example when the restriction of the domain is explicitly given. On the other hand the results are also connected to the examinations, where the equations are satisfied only almost everywhere (with respect to the Lebesgue-measure) on their domain. We also deal with characterization problems of probability theory, such as characterization problems of univariate distributions (for example characterizations of gamma, beta, normal and exponential distributions) as well as characterization problems of conditionally specified bivariate distributions. This book can be helpful for both mathematicians interested in mathematical analysis and researchers interested in characterization problems of probability distributions.
Low-frequency asymmetric vibrations a thin shell with a turning point Low-frequency asymmetric vibrations a thin shell with a turning point Новинка

Low-frequency asymmetric vibrations a thin shell with a turning point

Most problems in Applied Mathematics involving difficulties such as nonlinear governing equations and boundary conditions, variable coefficients and complex boundary shapes preclude exact solutions. Consequently exact solutions are approximated with ones using numerical techniques, analytical techniques or a combination of both. This book looks at the low frequency vibrations of a thin shell of revolution with a curvature which changes sign. Integrals of the equilibrium equations and stress-strain relations are represented in the form of asymptotic series and their solutions as a combination of the Airy function and its derivative.
Solution of Random Operator Equations and Inclusions Solution of Random Operator Equations and Inclusions Новинка

Solution of Random Operator Equations and Inclusions

Research in probabilistic operator theory generally includes the solutions of random operator equations and random operator inclusion, random extension theorems, limit theorems, measure theoretic problems, spectral theory of random operators and semi groups of random operators and their properties. Various ideas associated with random fixed point theory are used to form a particularly elegant approach for the solution of nonlinear random systems. Now this theory has become full- fledged research area lying at the intersection of nonlinear analysis and probability theory. In this monograpgh those aspects of random solution of random operator equations and random operator inclusion, which fall within the scope of investigation of random fixed point are discussed.
Symmetries and Exact Solutions OF Einstein Field Equations Symmetries and Exact Solutions OF Einstein Field Equations Новинка

Symmetries and Exact Solutions OF Einstein Field Equations

This book deals with applications of symmetry groups to solve physically important Einstein field equations, which are-the nondiagonal Einstein-Rosen metrics, the Einstein-Maxwell equations, Einstein-Maxwell equations for the magnetostatic fields, the Einstein-Maxwell equations for non-static Einstein and Rosen metrics, Einstein Vacuum equations for axially symmetric gravitational fields. To solve these highly nonlinear systems of partial differential equations (PDEs), Lie Classical method, symmetry reduction method and (G'/G)-expansion method are utilized. Symmetries are derived to reduce these systems of PDEs to ODEs and some exact solutions are obtained. Some of these solutions are also represented graphically.
Michael Greenberg D. Solutions Manual to accompany Ordinary Differential Equations Michael Greenberg D. Solutions Manual to accompany Ordinary Differential Equations Новинка

Michael Greenberg D. Solutions Manual to accompany Ordinary Differential Equations

Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order.
Basic Theory of Equation Basic Theory of Equation Новинка

Basic Theory of Equation

Stream of discoveries, gadgets, engineering marvels, and farsighted contrivances are poured by fecund imaginations of both Leonardo and Newton. Newton invented the reflecting telescope, Leonardo the helicopter; Newton, the binomial theorem, Leonardo, the parachute, submarine, and tank. So Newton's discoveries were expressed in equations. The theory of equations is a traditional course of mathematics which deals with the theory and solutions of polynomial and linear equations. The practical application of this subject has its greatest contribution to humankind to grow in an intense curiosity about the mathematical modeling. This book deals with the formation of equations and their corresponding solutions in accordance with numerical computation.
Renormalization Group Methods in Applied Mathematical Problems Renormalization Group Methods in Applied Mathematical Problems Новинка

Renormalization Group Methods in Applied Mathematical Problems

This book presents applications of the methods known as renormalization group (RG) and scaling in the physics literature to applied mathematics problems after a brief review of the methodology. The first part involves an application to a class of nonlinear parabolic differential equations. First, RG methods are described for determining the key exponents related to the decay of solutions to these equations. The determination of decay exponents is viewed as an asymptotically self similar process that facilitates an RG approach. The methods are also extended to higher order in the small coefficient of the nonlinearity. Finally, the RG results are verified in some cases by rigorous proofs and other calculations. In the second part, the application of RG technique to systems of equations describing interface problems is presented. The temporal evaluation of an interface separating two phases is analyzed for large time. The standard sharp interface problem in the quasi-static limit is studied. The characteristic length of a self-similar system that is a time dependent length scale characterizing the pattern growth is calculated by implementing RG procedure.
Nonlinear Euler-Poisson-Darboux Equations Nonlinear Euler-Poisson-Darboux Equations Новинка

Nonlinear Euler-Poisson-Darboux Equations

This book is devoted to study multidimensional linear and nonlinear partial differential equations. Among several methods to deal with higher dimensional linear partial differential equations, the elegant method of Spherical Means has spacial importance since this method reduces the higher dimensional equations to the one dimensional radial equations of Euler-Poisson-Darboux type which are well studied. Although this method is applicable only to the linear differential equations, by some special transformations, like the Cole-Hopf transformation and the Backlaund transformation, exact solutions of multidimensional nonlinear partial differential equations of the Spherical Liouville, Sine- Gordon and Burgers type are constructed.
On a mathematical model for case hardening of steel On a mathematical model for case hardening of steel Новинка

On a mathematical model for case hardening of steel

The applications of steel in industry are very diverse and widespread. The basic principle involved in heat treatment is the process of heating and cooling. The industrial process of case hardening aims to harden just the workpiece case, letting the inner part softer. The macrosopical model presented here takes into account the diffusion of carbon in the workpiece at austenitic phase, the slow diffusion at high temperature and the rapid cooling, which produces the formation of the martensitic microstructure. During this process, phase transformations in steel take place, influenced by the non homogeneous carbon distribution. The mathematical model presented here consists of a nonlinear evolution equation for the temperature, coupled with a nonlinear evolution equation for the carbon concentration, both coupled with two ordinary differential equations describing the evolution of phase fractions. Existence and uniqueness of solutions are investigated and some numerical simulations are presented.

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Features a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fields With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-world ODE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear ordinary differential equations. The author’s primary focus is on models expressed as systems of ODEs, which generally result by neglecting spatial effects so that the ODE dependent variables are uniform in space. Therefore, time is the independent variable in most applications of ODE systems. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for ODEs Models as systems of ODEs with explanations of the associated chemistry, physics, biology, and physiology as well as the algebraic equations used to calculate intermediate variables Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general ODE computation through various biomolecular science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.
Продажа m o korpusov a v ovchinnikov blow up of solutions of model nonlinear equations of mathematical physics лучших цены всего мира
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