Convex Splitting Runge–Kutta methods for phase-field models

Jaemin Shin, Hyun Geun Lee, June Yub Lee

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


In this paper, we present the Convex Splitting Runge–Kutta (CSRK) methods which provide a simple unified framework to solve phase-field models such as the Allen–Cahn, Cahn–Hilliard, and phase-field crystal equations. The core idea of the CSRK methods is the combination of convex splitting methods and multi-stage implicit–explicit Runge–Kutta methods. Our CSRK methods are high-order accurate in time and we investigate the energy stability numerically. We present numerical experiments to show the accuracy and efficiency of the proposed methods up to the third-order accuracy.

Original languageEnglish
Pages (from-to)2388-2403
Number of pages16
JournalComputers and Mathematics with Applications
Issue number11
StatePublished - 1 Jun 2017


  • Allen–Cahn equation
  • Cahn–Hilliard equation
  • Convex splitting
  • Implicit–explicit Runge–Kutta
  • Phase-field crystal equation


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