Title: Half-sweep RSOR iteration with three-point linear rational finite difference scheme for solving first-order Fredholm integro-differential equations

Authors: Ming-Ming Xu; Jumat Sulaiman; Labiyana Hanif Ali

Addresses: School of Mathematics and Information Technology, Xingtai University, 054000, Xingtai, Hebei, China ' Faculty of Science and Natural Resources, Universiti Malaysia Sabah, 88400, Kota Kinabalu, Sabah, Malaysia ' Faculty of Science and Natural Resources, Universiti Malaysia Sabah, 88400, Kota Kinabalu, Sabah, Malaysia

Abstract: In this paper, we establish the three-point newly half-sweep linear rational finite difference-quadrature discretisation scheme, which is the combination of the three-point half-sweep linear rational finite difference (3HSLRFD) scheme alone with the first-order quadrature scheme especially half-sweep composite-trapezoidal (HSCT) in discretising the first-order linear Fredholm integro-differential equation (FIDE). Based on this established discretisation scheme, the corresponding 3HSLRFD-HSCT approximation equation can be derived and then generate the large-scale and dense linear system. Furthermore, the numerical solution of the first-order linear FIDE can be obtained by implementing the half-sweep refinement of successive over-relaxation (HSRSOR) iterative method to solve the linear system. For the sake of comparison, the formulation of the full-sweep Gauss-Seidel (FSGS) and full-sweep refinement of successive over-relaxation (FSRSOR) methods are also presented as the control method. Finally, several numerical examples of the proposed problem are shown to demonstrate that the HSRSOR iterative approach gives the highest degree of supremacy in terms of number of iterations and execution time as compared to the other two existing methods.

Keywords: first-order integro-differential equations; half-sweep concept; RSOR iteration; linear rational finite difference; composite trapezoidal.

International Journal of Computing Science and Mathematics, 2023 Vol.17 No.2, pp.182 - 194

Accepted: 05 Feb 2021

Published online: 03 May 2023 *