Diagonally implicit multistage integration methods for pseudospectral solutions of the wave equation
type: Item
instance of: scholarly article
title: Diagonally implicit multistage integration methods for pseudospectral solutions of the wave equation
zbMATH Open document ID: 0958.65103
DOI: 10.1016/S0168-9274(99)00129-4
published in: Applied Numerical Mathematics
publication date: 2000-09-04T00:00:00Z
review text: The acoustic wave equation in two spatial dimensions is discretized spatially by a pseudospectral Chebyshev method, and the temporal integration is done by a diagonally implicit multistage method introduced by \textit{J.~C. Butcher} [Appl. Numer. Math. 11, No. 5, 347-363 (1993; Zbl 0773.65046)]. The use of collocation at the Chebyshev-Gauss-Lobatto points imposes a rather severe stability constraint on the time step. The computed examples indicate, however, that for problems with smooth solutions, this difficulty may be ameliorated by the fact that low-order polynomials may suffice.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 1462300
zbMATH Keywords: acoustic wave equation
zbMATH Keywords: pseudospectral Chebyshev method
zbMATH Keywords: implicit multistage method
zbMATH Keywords: collocation
zbMATH Keywords: stability
author: Zdzislaw Jackiewicz
author: R. A. Renaut
reviewed by: Gerald W. Hedstrom
MaRDI profile type: Publication
Wikidata QID: Q126656627
description: scientific article; zbMATH DE number 1462300