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 approx-
imation of the kernel, to simplify the integral operator and then discretization of the simpli ed
operator using a forward di erence formula. To analyze and verify the accuracy of the method, we
examine sample and benchmark problems with known exact solutions.