Numerical approximation for integral equations

Elias Deeba,Shishen Xie

doi:10.1155/s0161171204307301

Abstract

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.

Highlights

Adomian polynomial algorithm has been extensively used to solve linear and nonlinear problems arising in many interesting applications
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]: x b y(x) = f (x) + λ1 K1(x, t)g1 y(t) dt + λ2 K2(x, t)g2 y(t) dt, a a and analyze the solution
We first describe the algorithm of the decomposition method as it applies to a general nonlinear equation of the form y = f + N(y), (2.1)

Summary

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.

Results

Conclusion