Nonlinear stability of the implicit-explicit methods for the Allen-Cahn equation

Xinlong Feng, Huailing Song, Tao TANG*, Jiang Yang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

71 Citations (Scopus)


In this paper, we will investigate the first- and second-order implicitexplicit schemes with parameters for solving the Allen-Cahn equation. It is known that the Allen-Cahn equation satisfies a nonlinear stability property, i.e., the free-energy functional decreases in time. The goal of this paper is to consider implicit-explicit schemes that inherit the nonlinear stability of the continuous model, which will be achieved by properly choosing parameters associated with the implicit-explicit schemes. Theoretical justifications for the nonlinear stability of the schemes will be provided, and the theoretical results will be verified by several numerical examples.

Original languageEnglish
Pages (from-to)679-695
Number of pages17
JournalInverse Problems and Imaging
Issue number3
Publication statusPublished - Aug 2013

Scopus Subject Areas

  • Analysis
  • Modelling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

User-Defined Keywords

  • Allen-Cahn equation
  • Energy stability
  • Implicit-explicit scheme


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