Approximation Methods for Solutions of Differential and Integral Equations PDF Download
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Author: V. K. Dzyadyk
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110944693
Category : Mathematics
Languages : en
Pages : 332
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Book Description
No detailed description available for "Approximation Methods for Solutions of Differential and Integral Equations".
Author: V. K. Dzyadyk
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110944693
Category : Mathematics
Languages : en
Pages : 332
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Book Description
No detailed description available for "Approximation Methods for Solutions of Differential and Integral Equations".
Author: Hans-Jürgen Reinhardt
Publisher: Springer Science & Business Media
ISBN: 1461210801
Category : Mathematics
Languages : en
Pages : 412
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Book Description
This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite difference methods and of projection methods for approximating their variational formulations.
Author: Harold Cohen
Publisher: Springer Science & Business Media
ISBN: 1441998365
Category : Mathematics
Languages : en
Pages : 493
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Book Description
This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.
Author: Solomon Grigorʹevich Mikhlin
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 328
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Book Description
The aim of this book is to acquaint the reader with the most important and powerful methods of approximate solution of boundary-value problems (including the Cauchy problem) for differential equations, both ordinary and partial, as well as approximate methods for solution of the most frequently encountered types of integral equations: Fredholm, Volterra and singular one-dimensional. This covers the entire domain of classical applications of mathematical analysis to mechanics, engineering, and mathematical physics.
Author: Hans-Jürgen Reinhardt
Publisher: Springer
ISBN: 9780387962146
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite difference methods and of projection methods for approximating their variational formulations.
Author: M. A. Goldberg
Publisher: Springer Science & Business Media
ISBN: 1475714661
Category : Science
Languages : en
Pages : 351
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Book Description
Author: Michael A. Golberg
Publisher: Springer Science & Business Media
ISBN: 1489925937
Category : Mathematics
Languages : en
Pages : 428
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Book Description
In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.
Author: Madan Mohan Panja
Publisher: CRC Press
ISBN: 0429534280
Category : Mathematics
Languages : en
Pages : 466
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Book Description
Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It’s main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.
Author: C.T.H. Baker
Publisher: Elsevier
ISBN: 0080929559
Category : Mathematics
Languages : en
Pages : 559
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Book Description
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! This volume contains contributions in the area of differential equations and integral equations. Many numerical methods have arisen in response to the need to solve "real-life" problems in applied mathematics, in particular problems that do not have a closed-form solution. Contributions on both initial-value problems and boundary-value problems in ordinary differential equations appear in this volume. Numerical methods for initial-value problems in ordinary differential equations fall naturally into two classes: those which use one starting value at each step (one-step methods) and those which are based on several values of the solution (multistep methods).John Butcher has supplied an expert's perspective of the development of numerical methods for ordinary differential equations in the 20th century. Rob Corless and Lawrence Shampine talk about established technology, namely software for initial-value problems using Runge-Kutta and Rosenbrock methods, with interpolants to fill in the solution between mesh-points, but the 'slant' is new - based on the question, "How should such software integrate into the current generation of Problem Solving Environments?"Natalia Borovykh and Marc Spijker study the problem of establishing upper bounds for the norm of the nth power of square matrices.The dynamical system viewpoint has been of great benefit to ODE theory and numerical methods. Related is the study of chaotic behaviour.Willy Govaerts discusses the numerical methods for the computation and continuation of equilibria and bifurcation points of equilibria of dynamical systems.Arieh Iserles and Antonella Zanna survey the construction of Runge-Kutta methods which preserve algebraic invariant functions.Valeria Antohe and Ian Gladwell present numerical experiments on solving a Hamiltonian system of Hénon and Heiles with a symplectic and a nonsymplectic method with a variety of precisions and initial conditions.Stiff differential equations first became recognized as special during the 1950s. In 1963 two seminal publications laid to the foundations for later development: Dahlquist's paper on A-stable multistep methods and Butcher's first paper on implicit Runge-Kutta methods.Ernst Hairer and Gerhard Wanner deliver a survey which retraces the discovery of the order stars as well as the principal achievements obtained by that theory.Guido Vanden Berghe, Hans De Meyer, Marnix Van Daele and Tanja Van Hecke construct exponentially fitted Runge-Kutta methods with s stages.Differential-algebraic equations arise in control, in modelling of mechanical systems and in many other fields.Jeff Cash describes a fairly recent class of formulae for the numerical solution of initial-value problems for stiff and differential-algebraic systems.Shengtai Li and Linda Petzold describe methods and software for sensitivity analysis of solutions of DAE initial-value problems.Again in the area of differential-algebraic systems, Neil Biehn, John Betts, Stephen Campbell and William Huffman present current work on mesh adaptation for DAE two-point boundary-value problems.Contrasting approaches to the question of how good an approximation is as a solution of a given equation involve (i) attempting to estimate the actual error (i.e., the difference between the true and the approximate solutions) and (ii) attempting to estimate the defect - the amount by which the approximation fails to satisfy the given equation and any side-conditions.The paper by Wayne Enright on defect control relates to carefully analyzed techniques that have been proposed both for ordinary differential equations and for delay differential equations in which an attempt is made to control an estimate of the size of the defect.Many phenomena incorporate noise, and the numerical solution of
Author: G. Micula
Publisher: Springer Science & Business Media
ISBN: 9780792318903
Category : Mathematics
Languages : en
Pages : 426
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Book Description
Many important phenomena are described and modeled by means of differential and integral equations. To understand these phenomena necessarily implies being able to solve the differential and integral equations that model them. Such equations, and the development of techniques for solving them, have always held a privileged place in the mathematical sciences. Today, theoretical advances have led to more abstract and comprehensive theories which are increasingly more complex in their mathematical concepts. Theoretical investigations along these lines have led to even more abstract and comprehensive theories, and to increasingly complex mathematical concepts. Long-standing teaching practice has, however, shown that the theory of differential and integral equations cannot be studied thoroughly and understood by mere contemplation. This can only be achieved by acquiring the necessary techniques; and the best way to achieve this is by working through as many different exercises as possible. The eight chapters of this book contain a large number of problems and exercises, selected on the basis of long experience in teaching students, which together with the author's original problems cover the whole range of current methods employed in solving the integral, differential equations, and the partial differential equations of order one, without, however, renouncing the classical problems. Every chapter of this book begins with the succinct theoretical exposition of the minimum of knowledge required to solve the problems and exercises therein.
