A numerical method to solve a class of linear integro-differential equations with weakly singular kernel

Abstract

In this paper, a collocation method based on the Bessel polynomials is introduced for the approximate solution of a class of linear integro-differential equations with weakly singular kernel under the mixed conditions. The exact solution can be obtained if the exact solution is polynomial. In other cases, increasing number of nodes, a good approximation can be obtained with applicable errors. In addition, the method is presented with error and stability analysis. Copyright (c) 2012 John Wiley & Sons, Ltd.