Applied Singular Integral Equations: 1st Edition (Hardback) book cover

Applied Singular Integral Equations

1st Edition

By B. N. Mandal, A. Chakrabarti

CRC Press

270 pages

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Hardback: 9781578087105
pub: 2011-05-02
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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

About the Authors

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

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
SCI086000
SCIENCE / Life Sciences / General