Solutions of convolution integral and Fredholm integral equations via double Fourier series

Abstract

Double Fourier series are developed to approximate the solutions of the convolution integral and Fredholm integral equations. Properties of Fourier series are first briefly presented, and the operational matrix of integration together with the product operational matrix is utilized to reduce the computation of integral equations to a set of simultaneous linear algebraic equations. The method is computationally very attractive, and applications are demonstrated through illustrative examples.