Contributed Session 2:  PDEs and Applications
Maximum principle and energy stablity preserving explicit scheme for solving Allen-Cahn equation
Seunggyu Lee
Korea University
Korea
  Co-Author(s):    Seunggyu Lee, Woonjae Hwang
  Abstract:
 

We propose an explicit linear scheme to solve the Allen--Cahn equation that satisfies energy stability and maximum principle. Our approach is based on a finite-difference spatial discretization, and we prove the maximum principle without any time-step restriction. The proposed method can be easily extended to the 2nd order accuracy in time. Numerical experiments demonstrate its accuracy, energy stability, and maximum principle.