Approximation Solution For Second Order Linear Fredholm Integro-Differential Equations By Implementing Half-Sweep Gauss-Seidel Method

Abstract

This paper provides an overview of the formulation, analysis and implementation of the Half-Sweep Gauss-Seidel (HSGS) method for solving second order linear Fredholm Integro-differential equation (SOLFIDE) based on backward difference (BD) and repeated trapezoidal (RT) approximation schemes. In fact, the formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) method, also known as standard Gauss-Seidel, are presented to show the significant result of proposed method. The HSGS method has been shown to converge rapidly as compared to the FSGS method. Finally some numerical tests were demonstrated to show that the HSGS method is superior to the FSGS method.