Two- Grid Method for Solving Elliptic Partial Differential Equations and its Comparison with Gauss–Seidel and SOR Methods

Abstract

This paper investigates the two-grid method for solving elliptic partial differential equations using the finite difference method, which leads to a linear system that is solved by the Gauss–Seidel and Successive Over-Relaxation (SOR) methods. The two-grid method is then applied to these iterative schemes in order to accelerate the convergence process. A numerical comparison is carried out between the two-grid method and the Gauss–Seidel and SOR methods in terms of the convergence rate, number of iterations, and accuracy of the numerical solution, in order to demonstrate the efficiency of the two-grid method in solving linear systems.