New analysis of the du Fort-Frankel methods

Neta Corem, Adi Ditkowski

Research output: Contribution to journalArticlepeer-review

Abstract

In 1953 Du Fort and Frankel (Math. Tables Other Aids Comput., 7(43):135-152, 1953) proposed to solve the heat equation u t =u xx using an explicit scheme, which they claim to be unconditionally stable, with a truncation error is of order of τ= O(k 2}+h 2+k 2h 2). Therefore, it is not consistent when k=O(h). In the analysis presented below we show that the Du Fort-Frankel schemes are not unconditionally stable. However, when properly defined, the truncation error vanishes as h,k→0.

Original languageEnglish
Pages (from-to)35-54
Number of pages20
JournalJournal of Scientific Computing
Volume53
Issue number1
DOIs
StatePublished - Oct 2012

Keywords

  • Du Fort-Frankel
  • Finite difference
  • Finite difference stability
  • Generalized Du Fort-Frankel

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