1st Edition

Applied Singular Integral Equations




ISBN 9781578087105
Published May 2, 2011 by CRC Press
270 Pages

USD $125.00

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Book Description

The book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution. It introduces the singular integral equations and their applications to researchers as well as graduate students of this fascinating and growing branch of applied mathematics.

Table of Contents

Preface
Introduction
Basic Definitions
Occurrence of singular integral equations
Some Elementary Methods of Solution of Singular Integral Equations
Abel integral equation and its generalization
Integral equations with logarithmic type of singularities
Integral equations with Cauchy type kernels
Application to boundary value problems in elasticity and fluid mechanics
Riemann-Hilbert Problems and Their Uses in Singular Integral Equations
Cauchy principal value integrals
Some basic results in complex variable theory
Solution of singular integral equations involving closed contours
Riemann Hilbert problems
Generalised Abel integral equations
Singular integral equations with logarithmic kernels
Singular integral equation with logarithmic kernel in disjoint intervals
Special Methods of Solution of Singular Integral Equations
Integral equations with logarithmically singular kernels
Integral equations with Cauchy type kernels
Use of Poincare’-Bertrand formula
Solution of singular integral equation involving two intervals
Hypersingular Integral Equations
Definitions
Occurrence of hypersingular integral equations
Solution of simple hypersingular integral equation
Solution of hypersingular integral equation of the second kind
Singular Integro-differential Equations
A class of singular integro-differential equations
A special type of singular integro-differential equation
Numerical solution of a special singular integro-differential equation
Approximate method based on polynomial approximation
Approximate method based on Bernstein polynomial basis
Galerkin Method and its Application
Galerkin method
Use of single-term Galerkin approximation
Galerkin method for singular integral equations
Numerical Methods
The general numerical procedure for Cauchy singular integral equation
A special numerical technique to solve singular integrals equations of first kind with Cauchy kernel
Numerical solution of hypersingular integral equation using simple polynomial expansion
Numerical solution of simple hypersingular integral equation using Bernstein polynomials as basis
Numerical solution of some classes of logarithmically singular integral equations using Bernstein polynomials
Numerical solution of an integral equation of some special type
Numerical solution of a system of generalized Abel integral equations
Some Special Types of Coupled Singular Integral Equations of Carleman Type and their Solutions
The Carleman singular integral equation
Solution of the coupled integral equations for large l
Solution of the coupled integral equations for any l
Bibliography
Subject index

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Author(s)

Biography

Mandal\, B. N.; Chakrabarti\, A.