Fourth-Order Crank-Nicolson Solution for Solving Diffusion Equation Using MSOR Iteration

Recently, numerous applications in engineering, sciences and economics can be modeled into diffusion equations problems. In this paper, we investigate the effectiveness of the Modified Successive Over-Relaxation (MSOR) iterative method in solving linear system generated from discretization of one-dimensional diffusion equation using fourth-order Crank-Nicolson discretization scheme. In order to access the performance results of the proposed iterative method with the fourth-order Crank-Nicolson scheme, other point iterative methods which are Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) also presented as reference method. Finally the numerical results obtained from the use of the fourth-order Crank-Nicolson discretization scheme, it can be pointed out that the MSOR iterative method is superior in terms of number of iterations, execution time, and maximum absolute error.