Jackel Vui Lung Chew and Jumat Sulaiman and Andang Sunarto (2021) Solving onedimensional porous medium equation using unconditionally stable halfsweep finite difference and SOR method. Mathematics and Statistics, 9 (2). pp. 166171. ISSN 23322071
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Solving onedimensional porous medium equation using unconditionally stable halfsweep finite difference and SOR methodABSTRACT.pdf Download (63kB) 

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Solving onedimensional Porous Medium Equation using unconditionally stable HalfSweep finite difference and SOR method.pdf Restricted to Registered users only Download (266kB)  Request a copy 
Abstract
A porous medium equation is a nonlinear parabolic partial differential equation that presents many physical occurrences. The solutions of the porous medium equation are important to facilitate the investigation on nonlinear processes involving fluid flow, heat transfer, diffusion of gasparticles or population dynamics. As part of the development of a family of efficient iterative methods to solve the porous medium equation, the HalfSweep technique has been adopted. Prior works in the existing literature on the application of HalfSweep to successfully approximate the solutions of several types of mathematical problems are the underlying motivation of this research. This work aims to solve the onedimensional porous medium equation efficiently by incorporating the HalfSweep technique in the formulation of an unconditionallystable implicit finite difference scheme. The noticeable unique property of HalfSweep is its ability to secure a low computational complexity in computing numerical solutions. This work involves the application of the HalfSweep finite difference scheme on the general porous medium equation, until the formulation of a nonlinear approximation function. The Newton method is used to linearize the formulated HalfSweep finite difference approximation, so that the linear system in the form of a matrix can be constructed. Next, the Successive Over Relaxation method with a single parameter was applied to efficiently solve the generated linear system per time step. Next, to evaluate the efficiency of the developed method, deemed as the HalfSweep Newton Successive Over Relaxation (HSNSOR) method, the criteria such as the number of iterations, the program execution time and the magnitude of absolute errors were investigated. According to the numerical results, the numerical solutions obtained by the HSNSOR are as accurate as those of the HalfSweep Newton GaussSeidel (HSNGS), which is under the same family of HalfSweep iterations, and the benchmark, NewtonGaussSeidel (NGS) method. The improvement in the numerical results produced by the HSNSOR is significant, and requires a lesser number of iterations and a shorter program execution time, as compared to the HSNGS and NGS methods.
Item Type:  Article 

Keyword:  Onedimensional porous medium equation , Halfsweep , Finite difference method , Newton , Successive over relaxation , Iterative method 
Subjects:  Q Science > QA Mathematics > QA1939 Mathematics > QA273280 Probabilities. Mathematical statistics 
Department:  CENTRE > Preparation Centre for Science and Technology 
Depositing User:  DG MASNIAH AHMAD  
Date Deposited:  29 Oct 2021 11:13 
Last Modified:  29 Oct 2021 11:13 
URI:  https://eprints.ums.edu.my/id/eprint/30899 
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