STABILITY AND CONVERGENCE OF A HYPERBOLIC TANGENT METHOD FOR SINGULAR INTEGRAL-EQUATIONS

In this paper we reexamine a previously proposed quadrature scheme. [VENTURINO], based on a formula proposed in [STENGER. 1976]. Our goal is to establish a stability result for the dominant singular integral equation of index one. and from it derive the error analysis for the proposed numerical method. The convergence of the method can then be extended to the first kind complete equation and to the equation of index zero. Finally the modifications necessary for applying this analysis to a recently proposed scheme for Hadamard finite part integral equations are examined. In all these proofs the necessary assumption we need to make is to restrict our considerations to a compact subset of the interval in which the equation is formulated. containing all the nodes A here the unknown is evaluated.