Quarter-sweep successive over-relaxation approximation to the solution of porous medium equations
Document Type
Article
Publication Date
1-1-2022
Abstract
This paper investigated the use of a successive over-relaxation parameter in a quarter-sweep finite difference approximation scheme. The performance of the developed quarter-sweep successive over-relaxation method is examined by considering a nonlinear partial differential equation, namely the porous medium equation. The main contribution of this paper is to present the stability, convergence and efficiency of the proposed method. Several initial-boundary value problems of the porous medium equation are solved to illustrate the efficiency of the proposed method. The numerical results showed that the quarter-sweep successive over-relaxation method is more efficient in reducing iterations and computational time than the standard and the existing numerical methods. In addition, the accuracy of the quarter-sweep successive over-relaxation method is comparable to the tested numerical methods. © 2022. IAENG International Journal of Applied Mathematics.All Rights Reserved
Keywords
Efficiency, Initial value problems, Newton-Raphson method, Nonlinear equations, Numerical methods, Partial differential equations, Porous materials, Approximation scheme, Finite difference approximations, Finite-difference methods, Newton's methods, Over relaxation parameter, Performance, Porous-medium equations, Quarter-sweep, Successive over relaxation, Successive over relaxation methods, Finite difference method
Divisions
Faculty_of_Business_and_Accountancy
Funders
Research Management Center, Universiti Malaysia Sabah
Publication Title
IAENG International Journal of Applied Mathematics
Volume
52
Issue
2
Publisher
International Association of Engineers