A Point Interpolation Meshless Method for the Numerical Solution of the Singularly Perturbed Integral and Integro-differential Equations

Abstract

Recently, there has been an increasing interest in the study of singular and perturbed systems. In this paper we propose a point interpolation mesh less method for solving singularly perturbed integro-differential integral equations. The method is based upon radial basis functions, using zeros of the shifted Legendre polynomial as the collocation points. The results of numerical experiments are compared with the exact solution in illustrative examples to confirm the accuracy and efficiency of the presented scheme