Resumen de An improved quadrature method for integral equations with logarithmic kernel

Rafael Celorrio Ibáñez, Víctor Domínguez Báguena

• In this paper we present a family of modified quadrature methods for the numerical approximation of integral equations of the first kind with logarithmic kernel. We prove the stability and the existence, under some smoothness assumptions for the exact solution, of an expansion in powers of the discretization parameter of the error. Using this expansion we deduce that a particular method reaches order three. Some comments on the use of Richardson extrapolation are given.