m attary - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

In this article, numerical solution of a linear Volterra integro- differential equations by means of the Shannon wavelets approximation is considered. The main purpose of this paper is to provide an efficient numerical approach for these equations based on the Collocation method incorporated with the connection coefficients of the Shannon wavelets. Properties of the connection coefficients of the Shannon wavelets are first presented. We design a numerical algorithm, which can transform Volterra integrodifferential equations to an algebraic systems. The convergence analysis of the method is also investigated. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.

Shannon wavelets approximation, Volterra integro-differential equations,Numerical verification