Numerical Method For Volterra Integral Equations Using A Finite Difference Method

Numerical Method For Volterra Integral Equations Using A Finite Difference Method

In this paper we present a numerical scheme for approximation of the smooth solutions of the 2nd kind Volterra integral equations with regular and weakly singular kernels. This method is based on the approximation of the kernel, to simplify the integral operator and then approximate the simplied operator by a forward difference formula after integration by parts. We test stability and accuracy of the method by sample and bench mark problems.