Enslaved Finite Difference Schemes for Nonlinear Dissipative PDEs

Don A. Jones, Len G. Margolin, Andrew C. Poje

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

We show how the accuracy of a given finite difference scheme approximating a dissipative nonlinear PDE may be improved. The numerical solutions are decomposed into two parts that may be interpreted as approximating the large and small scales of the true solutions. By enslaving the small scales in terms of the larger ones, we derive a new difference scheme that is, in general, more accurate than the original scheme. The new scheme is also more computationally efficient, provided that the time derivatives of the problem are not too large.

Original languageEnglish (US)
Pages (from-to)13-40
Number of pages28
JournalNumerical Methods for Partial Differential Equations
Volume12
Issue number1
DOIs
StatePublished - Jan 1996
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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