KSOR iterative method with quadrature scheme for solving system of Fredholm integral equations of second kind

Abstract

In this study, the system of second kind Fredholm integral equations has been discretized by using the first order quadrature scheme namely trapezoidal rule in order to construct the first order quadrature approximation equation. Next, the quadrature approximation equation obtained has been used to construct a system of linear equations. Three types of iterative methods were used to solve the system of linear equations such as Gauss-Seidel (GS), Successive Over Relaxation (SOR) and Kaudd Successive Over Relaxation (KSOR). For comparison purpose, two problems have been considered in this study in order to analyze the efficiency of these three proposed iterative methods for solving the problems. Based on the numerical results, it can be pointed out that KSOR is similar as SOR but both of these iterative methods are more efficient than GS method.

Keywords: quadrature scheme; system of Fredholm integral equations; KSOR iterative method