Discrete adomian decomposition method for solving fredholm integral equations of the second kind

Abstract

The nonlinear Fredholm integral equation (FIE) represents a large amount of nonlinear phenomena that usually produces a considerable amount of difficulties. This dissertation will display some methods used for solving this problem, such as an Adomian Decomposition Method (ADM) which is based on decomposing the solution to infinite series and numerical implementation of ADM for the special case when the kernel is separable. In addition, it discusses the process of applying the Discrete Adomian Decomposition Method (DADM) which gives the numerical solution at the nodes using quadrature rules like Simpsons rule and trapezoidal rule. The comparison of DADM with of both rules with the exact solution also are given. Furthermore the results from DADM, Triangles orthogonal functions (Tfs) and Rationalized Haar function (RHf) for two dimensional linear and nonlinear FIE of the second kind respectively are compared with exact solution. Hence the results obtained show equivalent accuracy when linear FIE of the second kind for two dimension were solved by DADM with Simpson’s rule and by Tfs. Whereas the results show of DADM with Simpson’s rule is more accurate than RHf to solve nonlinear FIE of the second kind for 2-D.