2 papers
math.NA2025
Maximum bound preservation of exponential integrators for Allen-Cahn equations
Chaoyu Quan, Pingzhong Zheng, Zhi Zhou
We develop and analyze a class of arbitrarily high-order, maximum bound preserving time-stepping schemes for solving Allen-Cahn equations. These schemes are constructed within the…
math.NA2024
Maximum bound principle and original energy dissipation of arbitrarily high-order rescaled exponential time differencing Runge-Kutta schemes for Allen--Cahn equations
Chaoyu Quan, Xiaoming Wang, Pinzhong Zheng +1
The energy dissipation law and the maximum bound principle are two critical physical properties of the Allen--Cahn equations. While many existing time-stepping methods are known to…