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

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.