Numerical solutions of Cauchy singular integral equations using generalized inverses

Abstract

Solving singular integral equations of Cauchy-type numerically involves solution of a linear system of equations. The number of collocation and quadrature points decides the size of the linear system and an n × n matrix is derived in most cases. Taking more collocation points may yield more accurate numerical solutions as in [1] and numerical difficulties arising in solving overdetermined system. We show that the coefficient matrix of the overdetermined system obtained by taking more collocation points than quadrature nodes have the generalized inverse.