@Article{JCM-34-5,
author = {Tao, Tang and Yang, Jiang},
title = {Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle},
journal = {Journal of Computational Mathematics},
year = {2016},
volume = {34},
number = {5},
pages = {451--461},
abstract = {<p style="text-align: justify;">It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes? To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which has been studied extensively for the phase field type equations. In this work, we will show that a stronger stability under the infinity norm can be established for the implicit-explicit discretization in time and central finite difference in space. In other words, this commonly used numerical method for the Allen-Cahn equation preserves the maximum principle.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1603-m2014-0017},
url = {https://global-sci.com/article/84566/implicit-explicit-scheme-for-the-allen-cahn-equation-preserves-the-maximum-principle}
}