A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations

Hong lin Liao, Tao Tang, Tao Zhou*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

97 Citations (Scopus)

Abstract

In this work, we present a second-order nonuniform time-stepping scheme for the time-fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete maximum principle, and by using the convolution structure of consistency error, we present sharp maximum-norm error estimates which reflect the temporal regularity. As our analysis is built on nonuniform time steps, we may resolve the intrinsic initial singularity by using the graded meshes. Moreover, we propose an adaptive time-stepping strategy for large time simulations. Numerical experiments are presented to show the effectiveness of the proposed scheme. This seems to be the first second-order maximum principle preserving scheme for the time-fractional Allen-Cahn equation.

Original languageEnglish
Article number109473
Pages (from-to)1-16
Number of pages16
JournalJournal of Computational Physics
Volume414
DOIs
Publication statusPublished - 1 Aug 2020

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Adaptive time-stepping strategy
  • Alikhanov formula
  • Discrete maximum principle
  • Sharp error estimate
  • Time-fractional Allen-Cahn equation

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