Stabilized integrating factor Runge-Kutta method and unconditional preservation of maximum bound principle

Jingwei Li, Xiao Li, Lili Ju, Xinlong Feng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)

Abstract

The maximum bound principle (MBP) is an important property for a large class of semilinear parabolic equations, in the sense that the time-dependent solution of the equation with appropriate initial and boundary conditions and nonlinear operator preserves for all time a uniform pointwise bound in absolute value. It has been a challenging problem to design unconditionally MBP-preserving high-order accurate time-stepping schemes for these equations. In this paper, we combine the integrating factor Runge-Kutta (IFRK) method with the linear stabilization technique to develop a stabilized IFRK (sIFRK) method, and we successfully derive sufficient conditions for the proposed method to preserve the MBP unconditionally in the discrete setting. We then elaborate some sIFRK schemes with up to the third-order accuracy, which are proven to be unconditionally MBP-preserving by verifying these conditions. In addition, it is shown that many classic strong stability-preserving sIFRK schemes do not satisfy these conditions except the first-order one. Extensive numerical experiments are also carried out to demonstrate the performance of the proposed method.

Original languageEnglish
Pages (from-to)A1780-A1802
Number of pages23
JournalSIAM Journal on Scientific Computing
Volume43
Issue number3
DOIs
Publication statusE-pub ahead of print - 18 May 2021

Keywords

  • High-order method
  • Integrating factor Runge-Kutta method
  • Maximum bound principle
  • Semilinear parabolic equations
  • Stabilization

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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