TY - JOUR
T1 - Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle
AU - Tang , Tao
AU - Yang , Jiang
JO - Journal of Computational Mathematics
VL - 5
SP - 451
EP - 461
PY - 2016
DA - 2016/10
SN - 34
DO - http://doi.org/10.4208/jcm.1603-m2014-0017
UR - https://global-sci.org/intro/article_detail/jcm/9806.html
KW - Allen-Cahn Equations, Implicit-explicit scheme, Maximum principle, Nonlinear energy stability.
AB - <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>