ON QUARTER-SWEEP FINITE DIFFERENCE SCHEME FOR ONE-DIMENSIONAL POROUS MEDIUM EQUATIONS
Jackel C. V. Lung, Jumat Sulaiman
Abstract
In this article, we introduce an implicit finite difference approximation for one-dimensional porous medium equations using Quarter-Sweep approach. We approximate the solutions of the nonlinear porous medium equations by the application of the Newton method and use the Gauss-Seidel iteration. This yields a numerical method that reduces the computational complexity when the spatial grid spaces are reduced. The numerical result shows that the proposed method has a smaller number of iterations, a shorter computation time and a good accuracy compared to Newton-Gauss-Seidel and Half-Sweep Newton-Gauss-Seidel methods.
Topics & Concepts
Quarter (Canadian coin)Porous mediumScheme (mathematics)Finite difference methodFinite difference schemeFinite differenceMathematicsPorosityMathematical analysisApplied mathematicsMaterials scienceHistoryComposite materialArchaeologyDifferential Equations and Numerical MethodsDifferential Equations and Boundary ProblemsAdvanced Mathematical Modeling in Engineering