1st Edition

Applied Singular Integral Equations

By B. N. Mandal, A. Chakrabarti Copyright 2012

    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.

    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
    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
    Subject index


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