Numerical solution of the Fredholm-Volterra integro-differential equations by the Shannon wavelets

This paper is concerned with obtaining the approximate solution of Fredholm-Volterra integro-differential equations. Properties of the Shannon wavelets and connection coefficients are first presented. We design a numerical scheme for these equations using the Galerkin method incorporated with the Shannon wavelets approximation and the connection coefficients. We will show that using this technique, the Fredholm-Volterra integro-differential equation is transformed to an infinite algebraic system, which can be solved by fixing a finite scale of approximation. The error analysis of the method is also investigated and the reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.