Submitted:
24 December 2018
Posted:
25 December 2018
You are already at the latest version
Abstract
In the paper, a fully discrete compact difference scheme with $O(\tau^{2}+h^{4})$ precision is established by considering the numerical approximation of the one-dimensional Allen-Cahn equation. The numerical solutions satisfy discrete maximum principle under reasonable step ratio and time step constraint is proved. And the energy stability for the fully discrete scheme is investigated. An example is finally presented to show the effectiveness of scheme.
Keywords:
Allen-Cahn equation
; compact difference scheme
; maximum principle
; energy stability
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