Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Discrete Maximum Principle and Energy Stability of Compact Difference Scheme for the Allen-Cahn Equation

Version 1 : Received: 24 December 2018 / Approved: 25 December 2018 / Online: 25 December 2018 (04:31:54 CET)

How to cite: Tian, D.; Jin, Y.; Lv, G. Discrete Maximum Principle and Energy Stability of Compact Difference Scheme for the Allen-Cahn Equation. Preprints 2018, 2018120294 (doi: 10.20944/preprints201812.0294.v1). Tian, D.; Jin, Y.; Lv, G. Discrete Maximum Principle and Energy Stability of Compact Difference Scheme for the Allen-Cahn Equation. Preprints 2018, 2018120294 (doi: 10.20944/preprints201812.0294.v1).

## 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

## Subject

MATHEMATICS & COMPUTER SCIENCE, Numerical Analysis & Optimization

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