An energy-stable generalized-α method for the Swift–Hohenberg equation

A. F. Sarmiento*, L. F.R. Espath, Philippe Antoine Vignal Atherton, L. Dalcin, M. Parsani, Victor Calo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-α method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift–Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time.

Original languageEnglish (US)
Pages (from-to)836-851
Number of pages16
JournalJournal of Computational and Applied Mathematics
StatePublished - Dec 15 2018


  • Energy stability
  • Numerical dissipation
  • Numerical instability
  • Pattern formation
  • Swift–Hohenberg equation
  • Time integration

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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