Numerical approximation for integral equations

A numerical algorithm, based on a decomposition technique, is presented for solving a class of nonlinear integral equations. The scheme is shown to be highly accurate, and only few terms are required to obtain accurate computable solutions. 1. Introduction. Adomian polynomial algorithm has been extensively used to solve linear and nonlinear problems arising in many interesting applications (see, e.g., [1, 2, 4, 5]). The algorithm (a decomposition method) assumes a series solution for the unknown quantity. It has been shown [3] that the series converges fast, and with only few terms, this series approximates the exact solution with a fairly reasonable error. In this note, we will adapt the algorithm and a modification version of the algorithm due to Wazwaz [7] to the solution of the nonlinear Volterra-Fredholm integral equations arising in the modeling of many applications [8]: