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4839 руб.
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Stochastic differential equations driven by Levy processes are used as mathematical models for random dynamic phenomena in applications arising from fields such as finance and insurance, to capture continuous and discontinuous uncertainty. For many applications, a stochastic differential equation does not have a closed-form solution and the weak Euler approximation is applied. In such numerical treatment of stochastic differential equations, it is of theoretical and practical importance to estimate the rate of convergence of the discrete time approximation. In this book, it is systematically investigated the dependence of the rate of convergence on the regularity of the coefficients and driving processes. The model under consideration is of a more general form than existing ones, and hence is applicable to a broader range of processes, from the widely-studied diffusions and stochastic differential equations driven by spherically-symmetric stable processes to stochastic differential equations driven by more general Levy processes. These processes can be found in a variety of fields, including physics, engineering, economics, and finance.
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7890 руб.
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The aim of this book is to present new series approximation methods for solving linear and nonlinear differential equations which arising in applied Sciences. These procedures applied on fluid dynamics problems, population model equations, oscillator problems, fractional order equation, batch reactor equation and the Riccati's differential equations. It is interesting to note that these methods give the analytic and numerical results.
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7763 руб.
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Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts.
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7790 руб.
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This book bring new solutions for various types of differential equations. Approximate analytic solution was obtained for system of differential equations specially that has chaotic behavior, delay differential equations, Schrodinger and coupled Schrodinger equation, fractional differential equations, differential algebraic equations and some other fluid mechanic models. Accurate and simple solution was presented via several modifications for homotopy analysis method.
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3549 руб.
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The approximation theory is a scope of mathematical analysis, which at its essence, is interested with the approximation of functions by simpler and more easily calculated functions. This theory has widely influenced such other areas of mathematics as orthogonal polynomials, partial differential equations, harmonic analysis, and wavelet analysis. Some modern applications include computer graphics, signal processing, economic forecasting, and pattern recognition.
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7790 руб.
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The solutions of impulsive differential equations (IDEs) are often discontinuous and are not integrable in the ordinary sense of the word as most hypotheses in differential equations normally assumed.This peculiarity makes (IDEs) not easily accessible to most existing concepts and theorems in the differential equations. Therefore the existing concepts, theories in Differential Equations need to be strengthened or new ones developed before applying to (IDEs).This book will be useful to Students and practitioners in the field and in the industry working on problems with impulsive attributes such as modeling/computer simulation of stock price and petroleum pricing, disaster management,harvesting problem, biomedical problems,engineering and so on. We utilized several interesting techniques in nonlinear analysis such as topological degree, compact operators, monotone-iterative technique, measure of non-compact maps, inequalities on cone and applied them to some practical problems including, Numerical approximation of solutions of impulsive differential equations and measure differential equations.
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2086.91 руб.
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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.
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6390 руб.
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An Introduction to Difference Equations, Differential Equations and Modeling give us an overview of studies in difference equations, differential equations with piecewise constant arguments and about some biological models. Here, they will see important relations between difference equations and differential equations with piecewise constant arguments, and biological events that are explained with mathematics. It is my hope that this work can be useful for students or researcher that are interested in Biomathematics.
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6890 руб.
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The importance of partial differential equations cannot be gainsaid. They are used in science and engineering. Many natural phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow etc occurring in science and engineering are described by partial differential equations. Partial differential equations often model mathematical systems where many variables exist. They are also used in statistics especially in the field of stochastic processes.
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7790 руб.
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Most problems in engineering and science are modeled by partial differential equations. These partial differential equations often contain non-linearities and stochastic terms which makes their analytical solution cumbersome and sometimes nonexistent. We present a basic intoduction to using semi-analtyic-numerical methods to solve this partial differential equations and hence understanding the nature of the problems they describe.
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3939 руб.
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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.
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1264.16 руб.
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The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
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3549 руб.
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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.
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5490 руб.
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This book covers the basic discussions on ordinary differential equations as fundamentals for the study of differential equations. This consists of the lessons together with sample problems and exercises at the end of every topic to give way the student for him to solve it. It is important that the student gain not just how to solve problems but most importantly, student should gain the concepts and ideas behind a certain topic. The author wishes that with this material, students can learn fully the knowledge of ordinary differential equations.
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4929 руб.
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The maximum principle is one of the most useful and best known tools employed in the study of partial differential equations. The maximum principle enables us to obtain information about uniqueness, approximation, boundedness and symmetry of the solution, bounds for the first eigenvalue, quantities of physical interest, necessary conditions of solvability for some boundary value problems, etc. The book is divided into two parts. Part I contains two chapters and presents the classical maximum principle for linear equations, some of its direct extensions for nonlinear equations and their applications. Part II of this book is divided into three chapters and is devoted to the P function method and its applications. The book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in elliptic partial differential equations.
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5790 руб.
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Ordinary differential equations are very essential for science and engineering students. In this book we present all types of first and second order ordinary differential equations and their solutions. Various examples that rendered the solutions understandable are given. Some applications of the ordinary differential equations in science and engineering are given. The book is written is a simple English language that will make it easy to be handled by all students.
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6890 руб.
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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.
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7790 руб.
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The text foundation of differential equations has the basic rudiments needed in the studying differential equations. Partial fractions, review of fundamental calculus, Laplace transform and its inverse, etc. have been treated in details in the preliminary chapter. In the main body many examples have been done with illustrations. Also exercises have been included to enable the reader access himself/herself and he/she progresses
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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.
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5490 руб.
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In this book the existence and uniqueness of fuzzy linear integro-differential equations of Volterra type is proved, also the analytic, approximated, and numerical solutions of these type of equations are discussed. Also the concept of fuzzy reduction formula to reduce fuzzy linear differential equations, fuzzy linear Volterra integral equations, and high order fuzzy linear integro-differential equations of Volterra type to first order fuzzy linear integro-differential equations of Volterra type are introduced. Tow type of fuzzy functions are used to define functions in each equation, fuzzy valued functions and fuzzy bunch function.
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8347.63 руб.
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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. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps and provides all the necessary details. Topical coverage includes: First-Order Differential Equations Higher-Order Linear Equations Applications of Higher-Order Linear Equations Systems of Linear Differential Equations Laplace Transform Series Solutions Systems of Nonlinear Differential Equations In addition to plentiful exercises and examples throughout, each chapter concludes with a summary that outlines key concepts and techniques. The book's design allows readers to interact with the content, while hints, cautions, and emphasis are uniquely featured in the margins to further help and engage readers. Written in an accessible style that includes all needed details and steps, Ordinary Differential Equations is an excellent book for courses on the topic at the upper-undergraduate level. The book also serves as a valuable resource for professionals in the fields of engineering, physics, and mathematics who utilize differential equations in their everyday work. An Instructors Manual is available upon request. Email sfriedman@wiley.com for information. There is also a Solutions Manual available. The ISBN is 9781118398999.
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5490 руб.
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In recent years there has been much research activity concerning the oscillation of solutions of delay differential equations. To a large extent, this is due to the realization that delay differential equations are important in applications. New applications which involve delay differential equations continue to arise with increasing frequency in the modelling of diverse phenomena in physics, biology, ecology, and physiology. In this book, we are concerned with the oscillation criteria of solutions of the second-order neutral differential equations. The book contains several and remarks illustrative examples as an application of our results. The obtained results essentially improve many known results in the literature.
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5790 руб.
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This book deals with the development and the analysis of numerical methods for the resolution of first order nonlinear differential equations of Hamilton-Jacobi type on irregular data. These equations arises for example in the study of front propagation via the level set methods, the Shape-from-Shading problem and, in general, in Control theory. Our contribution to the numerical approximation of Hamilton-Jacobi equations consists in the proposal of some semiLagrangian schemes for different kind of discontinuous Hamiltonian and in an analysis of their convergence and a comparison of the results on some test problems. In particular we will approach with an eikonal equation with discontinuous coefficients in a well posed case of existence of Lipschitz continuous solutions. Furthermore, we propose a semiLagrangian scheme also for a Hamilton-Jacobi equation of a eikonal type on a ramified space, for example a graph. This is a not classical domain and only in last years there are developed a systematic theory about this. We present, also, some applications of our results on several problems arise from applied sciences.
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4839 руб.
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This thesis is a study of inverse problems in fractional calculus where two major theorems of existence and uniqueness for the solution of fractional order integro differential equations have been proved in different approaches. Delay fractional order integro differential equations have also been discussed; some related results have been achieved. Also, three methods for solving inverse problems of fractional order integro differential equations with and without delay have been improved. These methods were illustrated by some examples. Some applications of problems associated with fractional order integro differential equations have been presented and solved by the improved methods. Finally, the results of the work have been discussed, and some recommended proposals and for future work have been suggested.
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6390 руб.
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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.
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4839 руб.
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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.
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5790 руб.
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This work includes a brief summary on differential equations which treated by the numerical solutions ,also it shows the classification of the ordinary differential equations with either integer or fractional order. It introduces powerful idea which is fractional differentiation matrix for solving the ordinary fractional differential equations.Beside, it introduces some numerical examples to confirm the accuracy and also the solution of initial and boundary value problems of fractional differential equations.
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7790 руб.
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Regularity theory is one of the most challenging problems in modern theory of partial differential equations. It has attracted peoples’ eyes for a long history. A classical method of partial regularity theory is the “freezing the coefficients” method. The proof is complex and troublesome. And the result obtained by this method is not optimal. In this book, we use the method of A-harmonic approximation, to consider regularity theory for nonlinear partial differential systems. The new method not only allows one to simplify the procedure of proof, but also to establish optimal regularity results directly. This book should be useful to professionals in partial differential equations.
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4139 руб.
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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.
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6690 руб.
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The present book addresses both advanced undergraduate or graduate students in mathematics who will participate in applied research. It might also be useful for the professional researchers in economics and biology, who use dynamical systems as modeling tools. In this book we try to provide procedures for applying general mathematical theory to concrete problems. Special attention is paid to numerical simulations. The applications from this book refer to the modeling of some processes from economy and biology. The models are described by differential equations with delay, stochastic differential equations with delay, uncertain differential equations with delay, fractional differential equations and fractional differential equation with delay in 1D, 2D and 3D.
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3549 руб.
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In this book you will find: - basic information related to some speciale functions (Gamma function, Beta function and Mittage-Leffler function) - Rules of Riemann- Liouville Fractional Integration. - Rules of Riemann- Liouville Fractional derivative. - Rules of Caputo Fractional derivative. - The Exact Solutions of Some Linear Fractional Differential Equations by Using Laplace Transform. - New method to solve Linear Fractional Differential Systems. In general, this book is considered the start point to students who want to learn fractional calculus in quickly easy way. moreover, it summarizes Laplace transform method to solve linear fractional differential equations, and introduces new method to solve system of fractional differential equations
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4929 руб.
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Problems in stochastic homogenization theory typically deal with approximating dierential operators with rapidly oscillatory random coefficients by operators with homogenized deterministic coefficients. Even though the convergence of these operators in multiple scales is well-studied in the existing literature in the form of a Law of Large Numbers, very little is known about their rate of convergence or their large deviations. This work establishes analytic results for the Gaussian correction in homogenization, and large deviation results for homogenization problems in random media. Several special cases are analyzed in detail.
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7790 руб.
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In chapter one, some new formulas for Caputo fractional derivatives of some elementary functions is given. The system of M-linear Voltera integro-fractional differential equations is reduced into a system of Voltera integral equations and the global and semi-global fundamental existence and uniquenas theorems and presented in Chapter two. In chapter three, some analytic and approximate methods are applied to treat such a system. In chapter four, Runge-Kutta methods with different orders are given to treat such a system. The convergence and stability are also investigated. In chapter five, special Chebyshev method is considered. In chapter six, conclusions and recommendations with comparisons between the methods are included.
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3549 руб.
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This book exclusively deals with the study of ideal convergence on different type of sequences spaces. The notion of “ideal convergence” is the generalization of the “statistical convergence”, introduced by H. Fast, which is an extension of the usual concept of sequential limits. The book also discusses the applications of these non-matrix methods in approximation theory. Written in a self-contained style, the book discusses in detail the methods of ideal convergence for single sequences along with applications and suitable examples. The last chapter gives some applications in approximation theory; the results are expected to find application in many other areas of pure and applied mathematics such as mathematical analysis, probability, fixed point theory and statistics.
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4839 руб.
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This project is on the numerical solution of partial differential equations. In this project a mathematical model is formulated together with its boundary conditions. Finite elements and finite difference methods are used to solve the problem. This project is intended for students taking mathematics courses especially Numerical solution of partial differential equations as a base on how to solve initial value problems numerically. This also will help students to explore some basics on matlab coding. It is my believe that any one who reads this project will benefit more.
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4839 руб.
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In this work some modifications of the iterative methods and new methods presented for solving non-linear equations. The order of convergence and corresponding error equations of our methods is derived analytically and with the help of Maple program. We noted that the convergence analysis of our methods have order of convergence three, four, five, six, seven and ten. The efficiency of the method is tested on several numerical examples. It is observed that our methods is comparable with the well-known existing methods and in many cases gives better results. Also, our methods are competing with the other iterative methods of simple roots for solving non-linear equations.
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4929 руб.
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This great book explicitly presents the numerical solution of general third order ordinary differential equations using both block method and Taylor series as predictors. Hybrid continuous Linear multi step methods were developed in an easy to know version. The author painstakingly demonstrated the appropriate use of hybrid block method and Taylor series as predictors for the solution of third order ordinary differential equations. These methods are more accurate and efficient than those of existing authors. The basic properties of the methods were well examined. Engineers, scientists and technicians will find it very useful in solving third order ordinary differential equations that are common in the field of science and engineering . It is a must read by every student, teacher and lover of mathematics (numerical analysis)!
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6890 руб.
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"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.
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4929 руб.
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We propose a new technique of the differential quadrature method to find numerical solutions of the different transport (convection-diffusion) equations with appropriate initial and boundary conditions. The present method is based on the Bernstein polynomials formula, which is used to construct the weighting coefficients matrices of differential quadrature method, the new methodology is called Bernstein differential quadrature method (BDQM). Also, we improved alternating direction implicit formulation of differential quadrature method (ADI-DQM), based on Bernstein differential quadrature method (ADI-BDQM) for solving transport (convection-diffusion) equations. The results show that the differential quadrature technique renewed can be used as a powerful, reliable, accurate and efficient numerical tool in solving the transport problems. Finally, the many appearance of nonlinear differential equations as transport model in some fields of applied mathematics makes it necessary to investigate methods of solution for such equations (numerical) and we hope that this work is a step in this direction. We sincerely hope this methods can be applied to a wider range of problems.
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6690 руб.
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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
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2359 руб.
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Infinite series and its convergence are basic concepts to know mathematics from very beginning of primary stage. It revolves in the minds of mathematicians all along life and creats visionary power to estimate everything that comes in the mind. This estimation is called approximation if put on sound footings with axioms. So every measurement by naked eye or ear or by sophisticated instruments is merely an approximation. It is hoped that in this monograph, approximation by wavelets will be useful in technology and communication science in coming days.
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9991.86 руб.
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Praise for the Second Edition «This book is an excellent introduction to the wide field of boundary value problems.»—Journal of Engineering Mathematics «No doubt this textbook will be useful for both students and research workers.»—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.
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7790 руб.
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This work examines the long run behaviour of both differential and difference, deterministic and stochastic linear Volterra equations. It is shown how observable phenomena in inefficient financial markets may be present in the solutions of stochastic functional differential equations. Firstly, we consider a stationary autoregressive conditional heteroskedastic (ARCH) process of order infinity. Necessary and sufficient conditions are established for the autocovariance function to lie in a particular class of slowly decaying sequences. Secondly, an admissibility theory of stochastic Volterra operators is developed which characterises sufficient conditions for almost sure convergence of stochastic Volterra integrals. This theory is applied to find the exact asymptotic behaviour of the solutions of a class of affine stochastic Volterra equations. Lastly the exact asymptotic behaviour of a stochastic differential equation with an average functional is determined for all real values of the parameters of the equation. This equation may be viewed as modelling the demand of traders in an inefficient financial market. A discretisation of this stochastic differential equation is also studied.
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1200.92 руб.
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Make sense of these difficult equations Improve your problem-solving skills Practice with clear, concise examples Score higher on standardized tests and exams Get the confidence and the skills you need to master differential equations! Need to know how to solve differential equations? This easy-to-follow, hands-on workbook helps you master the basic concepts and work through the types of problems you'll encounter in your coursework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every equation. You'll also memorize the most-common types of differential equations, see how to avoid common mistakes, get tips and tricks for advanced problems, improve your exam scores, and much more! More than 100 Problems! Detailed, fully worked-out solutions to problems The inside scoop on first, second, and higher order differential equations A wealth of advanced techniques, including power series THE DUMMIES WORKBOOK WAY Quick, refresher explanations Step-by-step procedures Hands-on practice exercises Ample workspace to work out problems Online Cheat Sheet A dash of humor and fun
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6890 руб.
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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.
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2849 руб.
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In this book we obtain an approximate solution for integral and integro-differential equations by Legendre wavelets and hybrid Legendre Block-Pulse functions. For this purpose, we employ operational matrices and using Galerkin method the integral and integro-differential equations are transformed to a linear system. Numerical examples are given to show applicability of the proposed approach.
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5490 руб.
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Some new types of nonlinear recurrence equations- algebraic, differential, integral and functional, are solved. Qualitative studies of the linear recurrence equations with variable coefficients are included. Applications to combinatorics are given, especially in connection with the sum of the generalized arithmetic-geometric series. Special topics such as circular convolution, partial fractions development and solving algebraic equations are also considered.
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6690 руб.
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In this work the existence and uniqueness theorem for single linear Volterra integral equation has been generalized to a system of linear Volterra integral equation of the second kind. Depending on Banach fixed point theorem, some new results have been proved.Also, a Taylor series expansion has been considered to solve a system of linear Volterra integral equations of the second kind and a system of linear Volterra integro-differential equations of the second kind.In addition, three different types of iterative methods have been formulated to solve above systems. Furthermore, we derive a new iterative method named by "modified successive approximation method" to solve above systems. By this modification a faster rate of convergence for the successive method is established. Also, we proved a new theorem about the existence, uniqueness and convergence of this method. Two different kinds of weighted residual methods have been applied to treat the above systems. Moreover, the spectral method has been modified and applied for solving the above systems.
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5790 руб.
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This textbook presents derivations and analytical solution methods for the basic linear partial differential equations that model transport, heat, diffusion, waves, vibration, and steady-state equilibrium (Laplace and Poisson equations). General theorems about solution properties (such as uniqueness and stability) are presented. Solution methods include Dirichlet's principle, separation of variables, Fourier series, and Green's functions. The book includes 61 problems with detailed solutions. The book is suitable for students of undergraduate mathematics, engineering, and science.
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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.
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This Project focuses on obtaining an approximation solution for solving a system of two dimensional linear Fredholm integral equations of the 2nd kind. Various numerical procedures are reformulated and applied for solving the above system with their newly written computer programs.such as;Numerical integrations methods for multiple integral (composite Simpson’s method & composite trapezoid method); four different types of weighted residual methods (collocation method, sub-domain method,least square method and Galerkin method) and two different types of Iterative methods (successive approximation method and Adomian decomposition method).
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This book provides a unified and accessible introduction to the numerical analysis of the first-order hyperbolic partial differential (transport) equations having point-wise delay as well as advance. For model problem in neuronal transport, which leads to advection equations with point-wise delay, the numerical methods have been derived and analyzed. Finite difference and finite volume approaches are used to develop the numerical techniques. Analysis is performed for the mathematical properties of the numerical approximations like estimates for stability and convergence. This book is developed as the result of the doctoral thesis of the author. The book is intended for a wide audience, and will be of great use both to numerical analysis and computational researcher in a variety of applications.
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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.
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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.
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The main objective to the study of theory of Partial Differential Equations (PDEs) is to insure or find out properties of solutions of PDE that are not directly attainable by direct analytical means. Certain function spaces have certain known properties for which solutions of PDEs can be classified. As a result, this work critically looked into some function spaces and their properties. We consider extensively, Lp-spaces, distribution theory and sobolev spaces. The emphasis is made on sobolev spaces, which permit a modern approach to the study of differential equations. Looking at the linear elliptic partial differential equations considered in this work, we see that the key is Lax-Milgram theorem and the full understanding of Sobolev spaces and its properties. We are able to remove the rigor associated with second order partial differential equations and present it in the form that we can easily handle through the function spaces discussed. The book is based on variational formulation of some Boundary Value Problems (PDEs) using some known theorem (Lax-Milgram Theorem) to ascertain the existence and uniqueness of weak solution to such linear Elliptic PDEs.
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This monograph is part of the field approximation theory, which covers a great deal of mathematical territory. The focus is dedicated to presenting various qualitative and quantitative versions of Voronovskaja’s type theorem applied for a large class of linear positive operators. Such issues have attracted the attention of thousands mathematicians in the last 80 years. Using this method we get the asymptotic behavior, the uniform convergence and the approximation order of the approximated functions for many well-known linear positive operators. It is interesting the fact that, we get some new and old results without using Popoviciu-Bohman-Korovkin's theorem for the convergence of a linear positive operator towards the identity operator or the O. Shisha and B. Mond result for the estimate of the approximation order.
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This book gives a comprehensive introduction to some modern problems of stochastic differential equations and its applications. The content can be divided into four primary parts.1) Generalization of standard growth condition of the diffusion coefficient of Ito equations.2) Two parametric Ito formula and Stochastic Goursat problem, 3) Cauchy problem for linear and nonlinear stochastic equations of the parabolic type. 4) Applications. Latter part deals with: Stochastic boundary value problem of the hyperbolic type, Stochastic vibration of mechanical systems under high frequency external random forces, Stochastic Schrodinger Equations, and Elements of Derivatives pricing.
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This book deals with some of the recent advances of the theory of Backward Stochastic Differential Equations (BSDE) with generators that grow quadratically in the control variable (qgBSDE). One starts by looking at the differentiability of these equations in its several parameters, the relevance of which is clarified as one builds new results for this class of equations, like path regularity or explicit convergence rates for truncated qgBSDE. Both these results are the first of its kind for qgBSDE, as they allow at last the required theoretical justification for the use of numerical methods to approximate the solution qgBSDE. The exponential transformation as a reduction method of qgBSDE to standard Lipschitz BSDE is also discussed. This leads once again to the theme of numerical approximation for this class of BSDE. The book concludes with a problem of optimal investment of insurance related derivatives written on non-tradable underlyings, but correlated with tradable assets. Dynamic utility-based indifference prices are calculated and closed form formulas for the prices and for the derivative hedges are given.
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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.
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New numerical methods, obtained by the Author, are presented. They solve more easier and accurate than the classical methods, the algebraic, polynomial, linear difference and differential equations, as well as some types of algebraic recurrence equations. High order numerical automatic differentiation is also considered. Generally, these methods are based on discrete convolution and deconvolution. Solved examples are included. Praise for the Second Edition «This book is an excellent introduction to the wide field of boundary value problems.»—Journal of Engineering Mathematics «No doubt this textbook will be useful for both students and research workers.»—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.