Comparisons of Newton-Cotes quadrature schemes with Half-Sweep SOR method for second kind linear Fredholm integral equations

Abstract

In this paper, we investigate the applications of two different schemes of Newton-Cotes quadrature method that is repeated trapezoidal (RT) and repeated Simpson’s 31 (RS1) schemes via Half-Sweep Successive Over-Relaxation (HSSOR) iterative method to solve second kind linear Fredholm integral equations. Furthermore, the derivation and implementation of the proposed method are also included. Numerical tests and comparisons with other existing methods are given to illustrate the effectiveness of the proposed method.