A finite difference method for the smooth solution of linear Volterra integral equations

Abstract

The present paper proposes a fast numerical method for the linear Volterra integral equations with<br />regular and weakly singular kernels having smooth solutions. This method is based on the approx-<br />imation of the kernel, to simplify the integral operator and then discretization of the simpli ed<br />operator using a forward di erence formula. To analyze and verify the accuracy of the method, we<br />examine sample and benchmark problems with known exact solutions.