High-order symmetric multistep cosine methods
type: Item
instance of: scholarly article
title: High-order symmetric multistep cosine methods
zbMATH Open document ID: 1267.65087
author: M. J. Moreta
author: Begoña Cano
published in: Applied Numerical Mathematics
publication date: 2013-03-04T00:00:00Z
review text: Multistep cosine methods constitute a subclass of exponential integrators, designed to integrate the linear and stiff part of problems of second order in time exactly. The purpose of the paper is to construct high-order symmetric methods within this family, designed for systems that arise after a pseudospectral discretization of periodic boundary problems defined by second-order partial differential equations when appropriate regularity conditions take place. As with other families of multistep methods, the phenomenon of numerical resonance also appears with these schemes: there are some particular values of the time step size \(h\) for which the error is much greater that for other values of \(h\). To avoid this effect, a simple filter technique is proposed without losing the order of consistency. Two particular multistep cosine methods of orders 8 and 10 are constructed in the paper, which are subsequently illustrated on a pair of numerical examples in comparison with Gauss methods of the same order. These examples suggest that the new methods are more efficient than Gauss integrators.
reviewed by: Fernando Casas
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L04
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35G30
zbMATH DE Number: 6140835
zbMATH Keywords: exponential integrators
zbMATH Keywords: second-order partial differential equations
zbMATH Keywords: symmetric methods
zbMATH Keywords: high accuracy
zbMATH Keywords: stiff equations
zbMATH Keywords: multistep cosine methods
zbMATH Keywords: pseudospectral discretization
zbMATH Keywords: periodic boundary problems
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.apnum.2012.11.005
OpenAlex ID: W1979637151
DOI: 10.1016/J.APNUM.2012.11.005
description: scientific article; zbMATH DE number 6140835