Caputo’s finite difference solution of fractional two-point boundary value problems using SOR iteration

Abstract

The aim of this paper deals with Caputo’s solution of fractional two-point boundary value problems by using second-order central difference discretization scheme and Caputo’s fractional operator to construct a Caputo’s finite differences approximation equation. Then this approximation equation was be used to generate a linear system. In this paper, the Successive Over-Relaxation (SOR) method has been considered as linear solver. To do this matter, this method is derive based on the Caputo’s approximation equation. Based on numerical results, solutions in this problem will show SOR method is requires less amount of number of iterations and computational time as compared with GS method. In term of number of iterations, performance analysis of SOR methods has drastically decreased between 95.00% and 99.99% with the execution time decline between 87.00% and 99.99% respectively as compared with GS method. The numerical result showed that the SOR method is more efficient as compared with GS method.