Quarter-Sweep Gauss-Seidel Method for Solving First Order Linear Fredholm Integro-differential Equations

Abstract

The purpose of this paper is to scrutinize the application of the Quarter-Sweep Gauss-Seidel (QSGS) method by using the quarter-sweep approximation equation based on backward difference (BD) and repeated trapezoidal (RT) formulas to solve first order linear Fredholm integro-differential equations. The formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) and Half-Sweep Gauss-Seidel (HSGS) iterative methods are also presented. Then some numerical tests are illustrated to show the effectiveness of QSGS method as compared to the FSGS and HSGS methods. Keywords: Integro-differential equations; Linear Fredholm equations; Finite difference; Quadrature formulas; Quarter-Sweep iteration. 2010 Mathematics Subject Classification 45J05; 65F10; 65Y20.