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

Document Type : Research Paper


1 of Mathematics, Faculty of Mathematical Sciences and Computer , Shahid Chamran University, Ahvaz, Iran.

2 Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.

3 School of Mathematics, Institute for Research in Fundamental Sciences, P. O. Box: 19395-5746, Tehran, Iran.


The present paper proposes a fast numerical method for the linear Volterra integral equations with regular and weakly singular kernels having smooth solutions. This method is based on the approximation of the kernel, to simplify the integral operator and then discretization of the simplified operator using a forward difference formula. To analyze and verify the accuracy of the method, we examine sample and benchmark problems with known exact solutions.