Order stars and the maximal accuracy of stable difference schemes for the wave equation

Rosemary Renaut, J. H. Smit

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The wave equation utt = c2uxx is solved by means of a three-time-level difference scheme, symmetric in time and space, of the form It was proved by Renaut that the maximal order of accuracy p of such a scheme is given by p 5 ≤ (s + S). In this paper we show that the requirement of stability does not reduce this maximal order. Our result is proved for S ≤ s by introducing an order star on the Riemann surface of the algebraic function associated with the scheme. 1980 Mathematics Subject Classification (1985 Revision). 65M10.

Original languageEnglish (US)
Pages (from-to)307-323
Number of pages17
JournalQuaestiones Mathematicae
Volume15
Issue number3
DOIs
StatePublished - Jul 1992

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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