Solution of nonlinear Volterra and Fredholm integro-differential equations by the rational Haar wavelet

Abstract

We successively apply the rational Haar wavelet  to solve the nonlinear Volterra integro-differential equations and nonlinear Fredholm integro-differential equations. Using the Banach fixed point theorem for these equations, we prove the convergence. In this method, no numerical integration is used. Numerical results are presented to show the effectiveness of this method.