Version 1
: Received: 24 December 2018 / Approved: 25 December 2018 / Online: 25 December 2018 (04:31:54 CET)
How to cite:
Tian, D.; Jin, Y.; Lv, G. Discrete Maximum Principle and Energy Stability of Compact Difference Scheme for the Allen-Cahn Equation. Preprints2018, 2018120294. https://doi.org/10.20944/preprints201812.0294.v1
Tian, D.; Jin, Y.; Lv, G. Discrete Maximum Principle and Energy Stability of Compact Difference Scheme for the Allen-Cahn Equation. Preprints 2018, 2018120294. https://doi.org/10.20944/preprints201812.0294.v1
Tian, D.; Jin, Y.; Lv, G. Discrete Maximum Principle and Energy Stability of Compact Difference Scheme for the Allen-Cahn Equation. Preprints2018, 2018120294. https://doi.org/10.20944/preprints201812.0294.v1
APA Style
Tian, D., Jin, Y., & Lv, G. (2018). Discrete Maximum Principle and Energy Stability of Compact Difference Scheme for the Allen-Cahn Equation. Preprints. https://doi.org/10.20944/preprints201812.0294.v1
Chicago/Turabian Style
Tian, D., Yuanfeng Jin and Gang Lv. 2018 "Discrete Maximum Principle and Energy Stability of Compact Difference Scheme for the Allen-Cahn Equation" Preprints. https://doi.org/10.20944/preprints201812.0294.v1
Abstract
In the paper, a fully discrete compact difference scheme with $O(\tau^{2}+h^{4})$ precision is established by considering the numerical approximation of the one-dimensional Allen-Cahn equation. The numerical solutions satisfy discrete maximum principle under reasonable step ratio and time step constraint is proved. And the energy stability for the fully discrete scheme is investigated. An example is finally presented to show the effectiveness of scheme.
Keywords
Allen-Cahn equation; compact difference scheme; maximum principle; energy stability
Subject
Computer Science and Mathematics, Discrete Mathematics and Combinatorics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.