A new second-order maximum-principle preserving finite difference scheme for Allen–Cahn equations with periodic boundary conditions

• DOI: 10.1016/j.aml.2020.106265
• Publication Date: 2020-02-05T16:51:55Z
• Authors: Tianliang Hou; Defeng Xiu; Wenzhu Jiang
• Keywords: Maximum principle; Finite difference scheme; Allen–Cahn equation; Periodic boundary conditions

Abstract This paper aims to present a new second-order maximum-principle preserving finite difference scheme for Allen–Cahn equations with periodic boundary conditions. The discrete maximum principle, the maximum-norm error estimate and the discrete energy stability of the proposed scheme are discussed. It is shown that the proposed scheme is unconditionally energy-stable by choosing proper parameters. A numerical experiment is performed to verify the theoretical results.