Applied Singular Integral Equations

ISBN: 9781578087105 出版年：2016 页码：274 Mandal, B N Chakrabarti, A CRC Press

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