An energy stable Runge–Kutta method for convex gradient problems

Jaemin Shin, June Yub Lee

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We propose a class of Runge–Kutta methods which provide a simple unified framework to solve the gradient flow of a convex functional in an unconditionally energy stable manner. Stiffly accurate Runge–Kutta methods are high order accurate in terms of time and also assure the energy stability for any time step size when they satisfy the positive definite condition. We provide a detailed proof of the unconditional energy stability as well as unique solvability of the proposed scheme. We demonstrate the accuracy and stability of the proposed methods using numerical experiments for a specific example.

Original languageEnglish
Article number112455
JournalJournal of Computational and Applied Mathematics
StatePublished - 15 Mar 2020

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.


  • Convex problem
  • Gradient flow
  • Positive definite condition
  • Stiffly accurate Runge–Kutta method
  • Unconditional energy stability
  • Unique solvability


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