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Article

Stability Analysis of the Explicit Difference Scheme for Richards Equation

1
School of Mathematical and Physical Sciences, Dalian University of Technology, Panjin 124221, China
2
Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
3
College of Sciences, Northeastern University, Shenyang 110819, China
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(3), 352; https://doi.org/10.3390/e22030352
Received: 6 January 2020 / Revised: 14 March 2020 / Accepted: 15 March 2020 / Published: 18 March 2020
(This article belongs to the Special Issue Applications of Nonlinear Diffusion Equations)
A stable explicit difference scheme, which is based on forward Euler format, is proposed for the Richards equation. To avoid the degeneracy of the Richards equation, we add a perturbation to the functional coefficient of the parabolic term. In addition, we introduce an extra term in the difference scheme which is used to relax the time step restriction for improving the stability condition. With the augmented terms, we prove the stability using the induction method. Numerical experiments show the validity and the accuracy of the scheme, along with its efficiency. View Full-Text
Keywords: Richards equation; explicit difference scheme; stability analysis Richards equation; explicit difference scheme; stability analysis
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MDPI and ACS Style

Liu, F.; Fukumoto, Y.; Zhao, X. Stability Analysis of the Explicit Difference Scheme for Richards Equation. Entropy 2020, 22, 352. https://doi.org/10.3390/e22030352

AMA Style

Liu F, Fukumoto Y, Zhao X. Stability Analysis of the Explicit Difference Scheme for Richards Equation. Entropy. 2020; 22(3):352. https://doi.org/10.3390/e22030352

Chicago/Turabian Style

Liu, Fengnan, Yasuhide Fukumoto, and Xiaopeng Zhao. 2020. "Stability Analysis of the Explicit Difference Scheme for Richards Equation" Entropy 22, no. 3: 352. https://doi.org/10.3390/e22030352

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