An explicit hybrid finite difference scheme for the Allen–Cahn equation

作者：

Highlights：

•

• We propose an explicit hybrid numerical method for solving the Allen–Cahn equation.

• The proposed method is based on an operator splitting method.

• We show the stability condition of the proposed numerical scheme.

• We show the pointwise boundedness of the solution under a solvability condition.

摘要

•We propose an explicit hybrid numerical method for solving the Allen–Cahn equation.•The proposed method is based on an operator splitting method.•We show the stability condition of the proposed numerical scheme.•We show the pointwise boundedness of the solution under a solvability condition.

论文关键词：Allen–Cahn equation,Finite difference method,Explicit hybrid method,Operator splitting method

论文评审过程：Received 6 April 2016, Revised 25 October 2017, Available online 5 March 2018, Version of Record 22 March 2018.

论文官网地址：https://doi.org/10.1016/j.cam.2018.02.026