The Numerical Treatment Of Integral Equations

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The Numerical Treatment Of Integral Equations

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Author : Christopher T. H. Baker
language : en
Publisher: Oxford University Press, USA
Release Date : 1977

The Numerical Treatment Of Integral Equations written by Christopher T. H. Baker and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Business & Economics categories.

This book is concerned with the numerical analysis of integral equations. We are not principally concerned with the abstract theory of integral equations, nor with applications of mathematics where integral equations arise, but the first chapter is devoted to a review of the theory of integral equations. The survey of certain aspects of numerical analysis in chapter 2 is intended to emphasize various topics which are of relevance in the study of numerical methods for integral equations.

Integral Equations

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Author : Wolfgang Hackbusch
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Integral Equations written by Wolfgang Hackbusch and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.

The Numerical Treatment Of Differential Equations

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Author : Lothar Collatz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Numerical Treatment Of Differential Equations written by Lothar Collatz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

VI methods are, however, immediately applicable also to non-linear prob lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of non-linear problems in the future. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far greater greater extent extent than than hitherto; hitherto; this this is is especially especially true true of partial differential equations and non linear problems. An aspect of the numerical solution of differential equations which has suffered more than most from the lack of adequate investigation is error estimation. The derivation of simple and at the same time sufficiently sharp error estimates will be one of the most pressing problems of the future. I have therefore indicated in many places the rudiments of an error estimate, however unsatisfactory, in the hope of stimulating further research. Indeed, in this respect the book can only be regarded as an introduction. Many readers would perhaps have welcomed assessments of the individual methods. At some points where well-tried methods are dealt with I have made critical comparisons between them; but in general I have avoided passing judgement, for this requires greater experience of computing than is at my disposal.

Numerical Treatment Of Partial Differential Equations

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Author : Christian Grossmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-11

Numerical Treatment Of Partial Differential Equations written by Christian Grossmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-11 with Mathematics categories.

This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It provides an introduction to the main principles of discretization and gives a presentation of the ideas and analysis of advanced numerical methods in the area. The book is mainly dedicated to finite element methods, but it also discusses difference methods and finite volume techniques. Coverage offers analytical tools, properties of discretization techniques and hints to algorithmic aspects. It also guides readers to current developments in research.

Linear And Nonlinear Integral Equations

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Author : Abdul-Majid Wazwaz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-24

Linear And Nonlinear Integral Equations written by Abdul-Majid Wazwaz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-24 with Mathematics categories.

Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.

The Numerical Treatment Of Integral Equations

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Author : Christopher T. H. Baker
language : en
Publisher:
Release Date : 1971

The Numerical Treatment Of Integral Equations written by Christopher T. H. Baker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.

Analytical And Numerical Methods For Volterra Equations

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Author : Peter Linz
language : en
Publisher: SIAM
Release Date : 1985-07-01

Analytical And Numerical Methods For Volterra Equations written by Peter Linz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-07-01 with Mathematics categories.

Presents integral equations methods for the solution of Volterra equations for those who need to solve real-world problems.

The Numerical Treatment Of Integral Equations

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Author : Christopher T. H. Baker
language : en
Publisher:
Release Date : 1978

The Numerical Treatment Of Integral Equations written by Christopher T. H. Baker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Integral equations categories.

Computational Methods For Integral Equations

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Author : L. M. Delves
language : en
Publisher: CUP Archive
Release Date : 1985

Computational Methods For Integral Equations written by L. M. Delves and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.

This textbook provides a readable account of techniques for numerical solutions.

Numerical Approximation Methods

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Author : Harold Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-28

Numerical Approximation Methods written by Harold Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-28 with Mathematics categories.

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.