Summation by parts operators for finite difference approximations of second derivatives

Ken Mattsson, Jan Nordström

Research output: Contribution to journalArticlepeer-review

294 Citations (Scopus)


Finite difference operators approximating second derivatives and satisfying a summation by parts rule have been derived for the fourth, sixth and eighth order case by using the symbolic mathematics software Maple. The operators are based on the same norms as the corresponding approximations of the first derivative, which makes the construction of stable approximations to general parabolic problems straightforward. The error analysis shows that the second derivative approximation can be closed at the boundaries with an approximation two orders less accurate than the internal scheme, and still preserve the internal accuracy.

Original languageEnglish
Pages (from-to)503-540
Number of pages38
JournalJournal of Computational Physics
Issue number2
Publication statusPublished - 20 Sept 2004
Externally publishedYes


  • Accuracy
  • Boundary conditions
  • High order finite difference methods
  • Numerical stability
  • Second derivatives

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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