A linear second-order finite difference scheme for the Allen-Cahn equation with a general mobility
Zirui Du, Tianlian Hou
School of Mathematics and Statistics, Beihua University, Jilin, China
Keywords: Allen-Cahn equation, general mobility, maximum bound principle, energy stability, error estimate
Abstract
In this paper, a linear second-order finite difference scheme is proposed for the Allen-Cahn equation with a general positive mobility. The Crank-Nicolson scheme and Taylor's formula are used for temporal discretization, and the central finite difference method is used for spatial approximation. The discrete maximum bound principle (MBP), the discrete energy stability and L∞-norm error estimation are discussed, respectively. Finally, some numerical examples are presented to verify our theoretical results.
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