Sinc collocation approximation of non-smooth solution of a nonlinear weakly singular Volterra integral equation

Abstract

A numerical method based on sinc collocation approximation for a class of nonlinear weakly singular Volterra integral equations of a second kind with non-smooth solution is given. The numerical method given here combines a sinc collocation method with an explicit iterative process that involves solving a nonlinear system of equations. We provide an error analysis for the method. It is shown that the approximate solution converges to the exact solution at the rate of M exp ( - c M ) , where M is the number of collocation points and c is some positive constant. Some numerical results for several test functions are given to confirm the accuracy and the ease of implementation of the method.