Numerical solution of partial integro-differential equation with a weakly singular kernel based on Sinc methods

Abstract

We study the formulation of a space–time Sinc collocation method based on single and double exponential transformations for the numerical solution of the partial integro-differential equation with a weakly singular kernel in one or two space dimensions. The space–time adjective means that the Sinc collocation technique is employed simultaneously in time and space. The error bounds are given which show the exponential convergence rate of the method. Numerical results reported show that the validity and effectiveness of the proposed algorithms are attained for singular problems.