An efficient method for a class of integro-differential equations with a weakly singular kernel

Abstract

In this work, a class of volterra integro-differential equation with a weakly singular kernel is discussed. The shifted Legendre Tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices. Also the convergence analysis and error estimation have been discussed and approved with the exact solution. Finally, several numerical examples are given to demonstrate the high accuracy of the method.