The maximal accuracy of stable difference schemes for the wave equation
type: Item
instance of: scholarly article
title: The maximal accuracy of stable difference schemes for the wave equation
zbMATH Open document ID: 0826.65079
DOI: 10.1007/BF01732980
author: R. A. Renaut
author: Kosie J. H. Smit
author: Rolf Jeltsch
published in: BIT
publication date: 1995-11-26T00:00:00Z
review text: The following symmetric full discretization \[ \sum^S_{j = -S} b_j U_{n+1, m+j} + \sum^s_{j = -s} a_j U_{n,m + j} + \sum^S_{j = -S} b_j U_{n - 1, m + j} = 0 \] for the wave equation \(u_{tt} = a^2 u_{xx}\) is investigated. It is well known that the maximal order of accuracy \(p\) of such a scheme is given by \(p \leq 2(s + S)\). The authors show that the requirement of stability does not reduce this maximal order for any pair \((s,S)\). Furthermore, Padé schemes are proved to be stable for \(0 < \mu < 1\), where \(\mu\) is the Courant number. These schemes can be implemented with high-order absorbing boundary conditions without reducing the range of \(\mu\).
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 773825
zbMATH Keywords: finite difference methods
zbMATH Keywords: Padé approximation
zbMATH Keywords: order star
zbMATH Keywords: Riemann surface
zbMATH Keywords: symmetric full discretization
zbMATH Keywords: wave equation
zbMATH Keywords: stability
zbMATH Keywords: absorbing boundary conditions
reviewed by: Qin Meng Zhao
MaRDI profile type: Publication
cites work: Q5558293
cites work: Q5185900
cites work: The Optimal Accuracy of Difference Schemes
cites work: Stability and accuracy of difference schemes for hyperbolic problems
cites work: An accuracy barrier for stable three-time-level difference schemes for hyperbolic equations
cites work: Accuracy Barriers of Two Time Level Difference Schemes for Hyperbolic Equations
cites work: Full Discretizations of $u_{tt} = u_{xx} $ and Rational Approximations to $\cosh \mu z$
cites work: ORDER STARS AND THE MAXIMAL ACCURACY OF STABLE DIFFERENCE SCHEMES FOR THE WAVE EQUATION
cites work: Absorbing boundary conditions, difference operators, and stability
cites work: ORDER STARS AND THE OPTIMAL ACCURACY OF STABLE, EXPLICIT DIFFERENCE SCHEMES
cites work: Barriers to Stability
cites work: Q3993078
cites work: Order stars and stability theorems
full work available at URL: https://doi.org/10.1007/bf01732980
OpenAlex ID: W2079314386
description: scientific article; zbMATH DE number 773825