The Explicit-Implicit-Null method: Removing the numerical instability of PDEs

Laurent Duchemin, Jens G Eggers

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)
349 Downloads (Pure)


A general method to remove the numerical instability of partial differential equations is presented. Two equal terms are added to and subtracted from the right-hand side of the PDE: the first is a damping term and is treated implicitly, the second is treated explicitly. A criterion for absolute stability is found and the scheme is shown to be convergent. The method is applied with success to the mean curvature flow equation, the Kuramoto-Sivashinsky equation, and to the Rayleigh-Taylor instability in a Hele-Shaw cell, including the effect of surface tension.

Original languageEnglish
Pages (from-to)37-52
Number of pages16
JournalJournal of Computational Physics
Early online date15 Jan 2014
Publication statusPublished - 15 Apr 2014


  • Birkhoff-Rott integral
  • Hele-Shaw
  • Kuramoto-Sivashinsky
  • Stiff set of partial differential equations
  • Surface tension

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