A HYPERBOLIC TANGENT QUADRATURE RULE FOR SOLVING SINGULAR INTEGRAL-EQUATIONS WITH HADAMARD FINITE PART INTEGRALS

Stenger's formula is adapted for singular integrals defined as Hadamard finite part. Convergence of the revised quadrature rule 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.