A hyperbolic tangent quadrature rule for solving singular integral equations with hadamard finite part integrals

Abstract

Stenger's formula is adapted for singular integrals defined as Hadamard finite part. Convergence of the revised quadrature is studied. A scheme for solving singular integral equations with Hadamard finite part integrals is proposed, based on the revised hyperbolic tangent quadrature rule. The integral equation is reduced to a system of linear equations, by taking the same points as quadrature nodes and collocation points. The coefficient matrix of the system is shown to be nonsingular.