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Computational Methods For Integral Equations

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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.

The Numerical Solution Of Integral Equations Of The Second Kind

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Author : Kendall E. Atkinson
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-28

The Numerical Solution Of Integral Equations Of The Second Kind written by Kendall E. Atkinson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-28 with Mathematics categories.

This book provides an extensive introduction to the numerical solution of a large class of 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.

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.

Computational Methods For Linear Integral Equations

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Author : Prem Kythe
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-04-26

Computational Methods For Linear Integral Equations written by Prem Kythe 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 2002-04-26 with Mathematics categories.

This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

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.

Integral Equations And Their Applications

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Author : Matiur Rahman
language : en
Publisher: WIT Press
Release Date : 2007

Integral Equations And Their Applications written by Matiur Rahman and has been published by WIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations.

Computational Methods For Linear Integral Equations

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Author : Prem Kythe
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28

Integral Equation Methods For Electromagnetic And Elastic Waves

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Author : Weng Cho Chew
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2009

Integral Equation Methods For Electromagnetic And Elastic Waves written by Weng Cho Chew and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Elastic waves categories.

Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods. Table of Contents: Introduction to Computational Electromagnetics / Linear Vector Space, Reciprocity, and Energy Conservation / Introduction to Integral Equations / Integral Equations for Penetrable Objects / Low-Frequency Problems in Integral Equations / Dyadic Green's Function for Layered Media and Integral Equations / Fast Inhomogeneous Plane Wave Algorithm for Layered Media / Electromagnetic Wave versus Elastic Wave / Glossary of Acronyms

Computational Methods For Integral Equations

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