[PDF] Approximate Methods For Solutions Of Differential And Integral Equations eBook

Author : V. K. Dzyadyk
Publisher : VSP
Page : 340 pages
File Size : 11,55 MB
Release : 1995
Category : Mathematics
ISBN : 9789067641944

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This book is the result of 20 years of investigations carried out by the author and his colleagues in order to bring closer and, to a certain extent, synthesize a number of well-known results, ideas and methods from the theory of function approximation, theory of differential and integral equations and numerical analysis. The book opens with an introduction on the theory of function approximation and is followed by a new approach to the Fredholm integral equations to the second kind. Several chapters are devoted to the construction of new methods for the effective approximation of solutions of several important integral, and ordinary and partial differential equations. In addition, new general results on the theory of linear differential equations with one regular singular point, as well as applications of the various new methods are discussed.

Author : Solomon Grigorʹevich Mikhlin
Publisher :
Page : 328 pages
File Size : 20,57 MB
Release : 1967
Category : Mathematics
ISBN :

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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 Science & Business Media
Page : 412 pages
File Size : 13,73 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461210801

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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 : V. K. Dzyadyk
Publisher : Walter de Gruyter GmbH & Co KG
Page : 332 pages
File Size : 46,71 MB
Release : 2018-11-05
Category : Mathematics
ISBN : 3110944693

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No detailed description available for "Approximation Methods for Solutions of Differential and Integral Equations".

Author : Harold Cohen
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 14,8 MB
Release : 2011-12-10
Category : Mathematics
ISBN : 1441998373

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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.