Новинка

3585 руб.

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.
Новинка

4631 руб.

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.
Новинка

5576 руб.

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.
Новинка

4631 руб.

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.
Новинка

6426 руб.

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.
Новинка

4631 руб.

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.
Новинка

5283 руб.

This book is concerned with the study of nonlinear water waves, which is one of the important observable phenomena in Nature. This study is related to the fluid dynamics, in general, and to the oceans dynamics in particular. The solutions of nonlinear PDEs with constant and variable coefficients, which describe the wave motion of undulant bores in shallow water, are investigated by using various analytical methods to illustrate the relation between solitary and water waves. The important ideas and results for nonlinear dispersive properties and solitons, which originated from the investigations of water waves, are discussed. The stability analysis for the second order system of PDEs is studied by using the phase plane method. In addition, we use perturbation methods to study the water wave problems for an incompressible fluid under the acceleration gravity and surface tension. The conservation laws of some PDEs are established. We illustrate the resulting solutions in several 3D-graphics showing the shock and solitary wave nature in the flow. This book contains many concepts of water wave motion and different mathematical methods that help researchers in the relevant topics.
Новинка

4631 руб.

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.
Новинка

4631 руб.

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
Новинка

5283 руб.

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.
Новинка

5576 руб.

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.
Новинка

6374 руб.

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.
Новинка

3393 руб.

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.
Новинка

6426 руб.

Vibrations and dynamic chaos are undesired phenomenon in structures as they cause the 4D. They are: disturbance, discomfort, damage and destruction of the system or the structure. For these reasons, money, time and effort are spent to eliminate or control vibrations,noise and chaos or to minimize them. The main object of this thesis is the investigation of the behavior two systems. They are simple and spring pendulums. A tuned absorber (passive control), in the transverse direction and/or the longitudinal one is connected to both systems to reduce the oscillations. Negative velocity feedback or its quadratic or cubic value is applied to the systems (active control). Also active control is applied to the systems via negative acceleration feedback or negative angular displacement or its quadratic or cubic value. Multiple scale is applied to determine approximate closed form solutions for the differential equations describing the systems. Both frequency response equations and the phase plane technique are applied to study systems stability. Optimum working conditions of both systems are extracted when applying both passive and active control, to be used in the design of such systems.
Новинка

2636 руб.

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
Новинка

6133 руб.

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.
Новинка

3393 руб.

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.
Новинка

3771 руб.

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.
Новинка

4631 руб.

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.
Новинка

4716 руб.

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.
Новинка

5380 руб.

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.
Новинка

6606 руб.

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.
Новинка

4631 руб.

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.
Новинка

14298 руб.

Nonlinear Theory of Pseudodifferential Equations on a Half-line,194
Новинка

6192 руб.

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.
Новинка

5576 руб.

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.
Новинка

6426 руб.

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.
Новинка

5576 руб.

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.
Новинка

3393 руб.

In this book, the biological systems were analyzed with the help of non-linear ordinary differential equations in the form of mathematical modeling. Firstly, I studied how one single species population model varies with respect to other models. Comparing different single species models, I investigated that logistic growth model is more realistic in comparison to the exponential growth model. Secondly, I studied mathematical modeling of two species population namely; predator-prey model and interspecific competition model. The models were analyzed and investigated through their solutions, steady states and trajectories in the phase plane. The two species system was found to be exhibited in stable periodic behavior for all initial conditions where populations were never considered zero. Ordinary differential equations contain a large field of distinct research in mathematical biology but my work has touched a little part of it. I believe that extensive and continuous involvement in mathematical biology research may result in to answer many questions for the development of this topic.
Новинка

7204 руб.

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.
Новинка

4631 руб.

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.
Новинка

5576 руб.

Existence of periodic solutions for higher order ordinary differential equations by the use of Leray- Schauder fixed-point technique depended mainly on the availability of suitable boundedness results. In some cases however, boundedness results were very difficult to establish because of the nature of the Lyapunov functions involved. In this thesis, existence results have been obtained using the Leray- Schauder fixed point technique and the integrated equations for the more general equations of the form : ... x + f (x?) + a1x? + a2x = p (t) x(4) + g ( ... x) + b1x? + b2x? + b3x = p (t) x(5) + c1x(4) + h x, x? , x?, ... x, x(4) ... x + c2x? + c3x? + c4x = p (t) where f = f (?x) , g = g ( ... x) , h = h
Новинка

4243 руб.

Analytical solutions of the nonlinear PDEs are presented to illustrate the wave propagation in granular materials. Theoretical investigations carried out for different values of the dispersion and microstructure parameters seem to show that the solutions of the models exhibit interesting features. Also, theoretical study of the two phase system of flow is presented to describe the fluid flow through porous granular matrix, and the various solutions of the magma equation are discussed to illustrate the evolution of porosity waves in the earth’s interior. In addition, we consider the fluidization of granular materials by a vibrating wall. The system is studied in the case of viscous and inviscid model. Grains are modeled as smooth rigid disks and the collisions are characterized by a constant normal restitution coefficient. The solutions of the van der Waals model of a granular system, exhibit appearance of bubbles. The instability is caused by the energy dissipation at collisions. Painleve analysis is introduced to investigate the integrability. Dispersion properties are also discussed. This book is suitable and will be interesting for all researchers in related fields.
Новинка

6417 руб.

The study of systems of nonlinear differential equations will be very useful to analyze the possible past or future outcomes with the help of present information in any natural dynamical systems. The present book studies some autonomous nonlinear systems of ordinary differential equations. It focuses on their applications to population dynamics problems in mathematical ecology. In particular, the following aspects are the main objectives of the present work: I) The stability of the equilibrium points. II) The behavior of solution around equilibrium points. The first chapter presents some standard basic concepts, definitions, notations, theorems and methods. The second chapter is devoted to the study of Kolmogrov models of population dynamics; Rosenweig-Mac Artur model; including competition and coexistence factors for mutual benefit of two species. The third and fourth chapters analyze the extended Lotka-Volterra predator-prey models including intraspecies factors. The behavior of solution around these equilibrium points are studied in detail.
Новинка

3771 руб.

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.
Новинка

4631 руб.

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.
Новинка

3960 руб.

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.
Новинка

7466 руб.

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.
Новинка

5283 руб.

It is known that Navier-Stokes equations is one of the most important equations in Fluid Mechanics and gas dynamics. On May 24, 2000, the Clay Mathematics Institute of Cambridge, Massachusetts (CMI) has named Navier-Stokes equations: Existence and smoothness of Navier-Stokes equations on $R^3$ as one of seven million problems. In this book, our aim is to study existence and asymptotic behavior of the Navier-Stokes equations and related models. The closely related models such as the Navier-Stokes-Poisson equations, Navier-Stokes-Korteweg equations,Jin-Xin model and Euler equations with damping are also studied. This book consists of three parts. Part 1 is to study the existence and zero dissipation limit of one-dimensional Navier-Stokes equations of compressible, isentropic and non-isentropic gases, and Jin-Xin model. The second part is about the existence and asymptotic behavior of the higher dimensional Navier-Stokes equations, Navier-Stokes-Poisson equations and Navier-Stokes-Korteweg equations. The third part is about the existence and asymptotic behavior of the isentropic and non-isentropic Euler equations with damping.
Новинка

4716 руб.

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.
Новинка

7466 руб.

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.
Новинка

6426 руб.

The understanding of the asymptotic behaviour of dynamical systems is one of the most important problems of modern mathematical physics. One way to treat this problem for systems having some dissipativity properties is to analyze the existence and structure of its global attractor. On some occasions, some phenomena are modelled by nonlinear evolutionary equations which do not take into account all the relevant information of the real systems. Instead some neglected quantities can be modelled as an external force which in general becomes time-dependent. For this reason, non-autonomous systems are of great importance and interest. Several models of reaction-diffusion equations in bounded and unbounded domains are analyzed in this book. Using the pullback theory so much for single-valued as for multi-valued non-autonomous dynamical systems, since this allows for more generality in the non-autonomous terms, the existence of pullback attractors for our models of reaction-diffusion equations is proved in this book.
Новинка

4631 руб.

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.
Новинка

4631 руб.

The nonlinear matrix equation X^{s}+A*X^{-s})A=Q, when A is a square matrix, Q is a square positive definite matrix and s an integer number, has been studied by several authors. Equations of this type arise in many problems of systems theory, discrete time control and in many applications in various research areas including filter design, ladder networks, dynamic programming, stochastic filtering and statistics. In the case that A is nonsingular and s=1, the associated matrix equation has many contributions in the theory, applications and numerical solution of the discrete algebraic Riccati equation. In this book, necessary and sufficient conditions for the existence of the Hermitian solutions are presented as well as an algebraic method based on the Riccati equation for the computation of these solutions is proposed. Inequalities for the eigenvalues of A, Q are presented. Bounds for the extreme eigenvalues of the minimal solution are derived. These results are verified through numerical experiments. This book concerns graduate students as well as researchers in the fields of Applied Mathematics, Electrical and Computer Engineering.
Новинка

4550 руб.

This book is mainly expository work but chapter three carries (3.1.28), (3.1.29) and (3.1.38) a little original calculation. The various chapters are organized as follows,Chapter one contains a brief review of general relativity.Chapter two Contains space and time manifold.Chapter three Contains an Exact Solution of Einstein's Equations where the theories of modern physics generally involve a mathematical model,defined by a certain set of rules for translating the mathematical result into meaningful statements about the physical world.Chapter four Contains a cosmological constant introduced into the description of the universe in terms of the general theory of relativity by Albert Einstein in order to make those models static.Chapter five deals with Friedman Model with cosmological constant and Chapter six contains the Cosmological Constant where cosmological constant was invented by Albert Einstein in 1917 already mention in different chapters. Einstein used his equations of general relativity to make cosmological models. He found that the model could not stay the some size, but needed to be either expansion or contraction.
Новинка

4631 руб.

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.
Новинка

3743.34 руб.

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.
Новинка

3865 руб.

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.
Новинка

6426 руб.

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
Новинка

5576 руб.

In this book, we study the validity of the maximum principle (one of the most useful and best known tools employed in the study of partial differential equations) for some nonlinear elliptic systems, with variable coefficients, involving the weighted p-Laplcaian operators on bounded and unbounded domains. Also, using a different methods like the nonlinear theory of monotone operators, subsuper solutions method and an approximation (perturbation) method, we study the existence of positive weak solutions for some nonlinear elliptic systems, with variable coefficients, involving the weighted p-Laplcaian operators on bounded and unbounded domains.
Новинка

4716 руб.

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.
Новинка

5283 руб.

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.
Новинка

3274 руб.

We introduce physical concepts of gradient, divergence, and curl, as a pre-requisite to understanding Maxwell’s equations. We then present the experimental laws of electricity and magnetism. These laws are described in terms of physical contents and their mathematical representations. Taken together, they suggest no new effects beyond the original experiments they represent. It is only when the displacement current is added that new physics emerges. This physics includes the prediction of the existence of electromagnetic waves which follow from Maxwell’s equations and transport energy and momentum through empty space by means of electromagnetic fields. We begin with electromagnetic wave equations in terms of electric scalar potential and magnetic vector potential, and then explain its physical meaning. Electromagnetic waves and their solutions are illustrated. Physical insight of magnetic vector potential is presented as electromagnetic momentum per unit charge of a test charge. We then describe spherical waves from a point source, electromagnetic waves in a dielectric medium, the complex refractive index, and finally the energy flow in the electromagnetic field.
Новинка

6374 руб.

Integrability of a dynamical system is a concept which is widely discussed for a long time in physics, mathematics and somewhat differently in different contexts. It can also be considered as a mathematical property that can be successfully used to obtain more predictive power and quantitative information to understand the system globally. Integrable models form a beautiful class of physical models in the sense that they are exactly solvable. There are various circumstances in which interest in integrability can arise. In past non-linear ordinary and partially differential equations are generally used to study for the description of natural phenomena, such as weather changes, growth of population, non-linear dynamical systems, solitary waves, propagation of light in optical fibre. The evolution of typical dynamical systems is often described by nonlinear ordinary and partial differential equations. One can learn a lot about nonlinear dynamical systems as the invariants are the analytic functions, and analytic results are much easier to use, to interpret and to generalize. Treating the integrable case as basic zeroth order exact solutions.
Новинка

2731 руб.

The subject of the research in this book algebraic geometry. Quadratic equality Z2=X2+Y2 and U2=X2+Y2+Z2 well known from the time of Pythagoras. However, the history of their research continues. The aim of this work is the analysis of the symmetry groups of solutions of quadratic equations on the basis of Periodical System of Natural Numbers. The book is the first to use the language of symmetry groups integers inhearent to physical phenomena and States: from the fine structure of crystals to arrangement of the periodic system of chemical elements and the solution of applied problems. Given in the book form of the calculation of the symmetry groups of quadratic identities Z2=X2+Y2 exhausts infinitely many solutions “Pythagorean” equalities and allows you to subdivide them according to the symmetry groups of numbers on 32 species - number equal to the number of point of crystallographic groups. Full package of solutions of quadratic equality U2=X2+Y2+Z2 has 230 options - known amount of all space groups of crystal symmetry.
Новинка

4716 руб.

This book deals with wide range of applications of continuous symmetry groups to some physically important systems which are: the coupled Klein-Gordon-Schrodinger equation with its generalized form, the Dullin-Gottwald-Holm Equation, the Generalized Bretherton equation with variable coefficients. For all the three different equations, we have derived some special type of solutions including traveling wave solutions, periodic solutions, kink wave solutions, solitons etc. and we have plotted some figures also to see the propogation and asymptotic behaviour of all types of waves.
Новинка

6606 руб.

In this book a novel 6-DOF vehicle dynamics/crash mathematical model and a lumped-mass occupant model are developed. The first model is used to show the effect of vehicle dynamic control systems (VDCS) on vehicle collision mitigation. The model allows studying the vehicle dynamics along with the vehicle crash structural dynamics. The anti-lock braking system (ABS), the active and semi-active suspension control systems (ASC and SASC) are developed and co-simulated with the model. The front-end structure is modelled as non-linear springs. The second model aims to predict the effect of the vehicle dynamics control system on the kinematics of the occupant. The Lagrange equations are used to solve that model owing to the complexity of the obtained equations of motion. The mathematical models and their associated equations of motion are developed and solved numerically to carry out this analysis. Validation of the vehicle crash structure and the occupant models are achieved to ensure that the models are reliable.
Новинка

5661 руб.

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.
Новинка

6606 руб.

It is well known that the differential equations fined a wide range of application in biological, physical, social and engineering. The interest on second order differential equations is due, in large part,to the fact that many physical systems are modeled by second order ordinary differential equations. For example, the so -called Emden-Fowler equation arises in the study of gas dynamics and fluid mechanics. The equation appears also in the study of relativistic mechanics, nuclear physics and in the study of chemically reacting systems.So, finding the solutions of the differential equations or deducing important characteristics of it has received the attention of many authors.In this work,via Integral averaging technique and Interval technique, we presented sufficient conditions for the oscillatory of the second order nonlinear differential equation with distributed deviating argument. Our results improve and extend some known results in the literature. Some illustrating examples are also provided to show the importance of our results.
Новинка

6201 руб.

In this work, we study the existence and uniqueness of weak solutions to the continuous coagulation and multiple fragmentation equations for large classes of kernels. A brief mathematical survey on the well-posedness of the equations under binary fragmentation is given. Later, a uniqueness theorem is proved for mass conserving solutions to the continuous coagulation and binary fragmentation equation under strong fragmentation. Furthermore, we develop the convergence analysis of sectional methods for solving the non-linear pure coagulation equation. Here we examine the most popular of all sectional methods the fixed pivot technique. Finally, we demonstrate practical significance of the mathematical results by performing a few numerical experiments. The fixed pivot technique gives a consistent over prediction of the solution for the large size particles when applied on coarse grids. To overcome this problem, the cell average technique was used which preserves all advantages of the fixed pivot technique and improves the numerical results. 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.