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- Title
A Reduced High-Order Compact Finite Difference Scheme Based on POD Technique for the Two Dimensional Extended Fisher-Kolmogorov Equation.
- Authors
Baozou Xu; Xiaohua Zhang; Daobin Ji
- Abstract
In this paper, we mainly utilize the reduced sixorder compact finite difference scheme (R-CFDS6) based on proper orthogonal decomposition (POD) and operator splitting method (R-CFDS6-OSM) to solve the two-dimensional Fisher-Kolmogorov equation and extended Fisher-Kolmogorov equation. Toward this end, the CFDS6 is built to attain high accuracy for one-dimensional extended Fisher-Kolmogorov equation. Then by means of the operator splitting method, the two-dimensional extended Fisher-Kolmogorov equation has been converted into a succession of one-dimensional equations successfully, which can be solved easily with CFDS6 compared with Alternating direction implicit method. Finally, by POD method, we develop the R-CFDS6-OSM with fewer unknowns and sufficiently high accuracy to improve the computational efficiency of CFDS6 and furnish the algorithm procedure of R-CFDS6-OSM. Some numerical examples are carried out to validate the high accuracy, effectiveness and feasibility of the R-CFDS6-OSM for the numerical solution of 2D Fisher-Kolmogorov equation.
- Subjects
PROPER orthogonal decomposition; HIGH-dimensional model representation; ALGORITHMS; EQUATIONS; FINITE differences
- Publication
IAENG International Journal of Applied Mathematics, 2020, Vol 50, Issue 3, p122
- ISSN
1992-9978
- Publication type
Article