The maximal accuracy of stable difference schemes for the wave equation

Rolf Jeltsch, Rosemary Renaut, Kosie J H Smit

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider three time-level difference schemes, symmetric in time and space, for the solution of the wave equation, utt =c2uxx, given by {Mathematical expression} It has already been proved that the maximal order of accuracy p of such schemes is given by p ≤ 2(s + S). In this paper we show that the requirement of stability does not reduce this maximal order for any choice of the pair (s, S). The result is proved by introducing an order star on the Riemann surface of the algebraic function associated with the scheme. Furthermore, Padé schemes, with S = 0, s > 0, and s = 0, S > 0, are proved to be stable for 0 < μ < 1, where μ is the Courant number. These schemes can be implemented with high-order absorbing boundary conditions without reducing the range of μ for which stable solutions are obtained.

Original languageEnglish (US)
Pages (from-to)83-115
Number of pages33
JournalBIT Numerical Mathematics
Volume35
Issue number1
DOIs
StatePublished - Mar 1995

Fingerprint

Wave equations
Difference Scheme
Stars
Wave equation
Boundary conditions
Maximal Order
Absorbing Boundary Conditions
Algebraic function
Stable Solution
Riemann Surface
Star
Higher Order
Requirements
Range of data

Keywords

  • accuracy
  • finite difference methods
  • order stars
  • Padé approximants
  • Riemann surface
  • stability
  • wave equation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Software
  • Computer Graphics and Computer-Aided Design

Cite this

The maximal accuracy of stable difference schemes for the wave equation. / Jeltsch, Rolf; Renaut, Rosemary; Smit, Kosie J H.

In: BIT Numerical Mathematics, Vol. 35, No. 1, 03.1995, p. 83-115.

Research output: Contribution to journalArticle

Jeltsch, Rolf ; Renaut, Rosemary ; Smit, Kosie J H. / The maximal accuracy of stable difference schemes for the wave equation. In: BIT Numerical Mathematics. 1995 ; Vol. 35, No. 1. pp. 83-115.
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