Convex Splitting Runge–Kutta methods for phase-field models

Jaemin Shin, Hyun Geun Lee, June Yub Lee

Research output: Contribution to journalArticlepeer-review

31 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

Bibliographical note

Funding Information:
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by Ministry of Education (MOE) and Ministry of Science and ICT and Future Planning (MSIP) (2009-0093827, 2015-003037).

Publisher Copyright:
© 2017 Elsevier Ltd


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


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