ORTHOGONAL POLYNOMIALS APPLIED TO THE SOLUTION OF SINGULAR INTEGRAL EQUATIONS
Abstract
Orthogonal polynomial methods are developed for the numerical solution of singular integral equations with Cauchy kernel. By considering an appropriate weight function, the singular integral operator with variable coefficients is shown to map one set of orthogonal polynomials to another set of orthogonal polynomials. Special properties of these orthogonal polynomial sets are investigated. The singular integral operator is defined on a weighted L('2)-space and characterized as unitary, isometric, or bounded with norm 1 (depending on the index). Quadrature, collocation, and Galerkin methods using these orthogonal polynomials are described. Convergence proofs and some error estimates are given. Numerical results for a variable coefficient example are given.
Degree
Ph.D.
Subject Area
Mathematics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.