EGSOR Iterative Method for the Fourth-Order Solution of One-Dimensional Convection-Diffusion Equations

In this paper, the effectiveness of two-point Explicit Group Successive Over-Relaxation (EGSOR) iterative method in obtaining the approximate solution of one-dimensional (1D) convection-diffusion equations with the fourth-order implicit finite difference scheme is investigated. For the fourth-order solution of the proposed problems, the combination of second-order and fourth-order implicit finite difference approximation equations have been used to derive the generated pentadiagonal linear system. For comparison purposes, other point iterative methods which are Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) are also included as control methods. Three numerical examples have been considered to access the efficiency of the proposed iterative method. Finally, from the numerical results obtained, it can be concluded that the two-point EGSOR iterative method shows superiority in terms of number of iterations and execution time in comparison to the other iterative methods.