A fast spectral algorithm for nonlinear wave equations with linear dispersion
type: Item
instance of: scholarly article
title: A fast spectral algorithm for nonlinear wave equations with linear dispersion
zbMATH Open document ID: 0937.65109
author: Bengt Fornberg
author: Tobin A. Driscoll
published in: Journal of Computational Physics
publication date: 2000-05-17T00:00:00Z
review text: The authors presented an easily implemented time stepping strategy for spatially spectral numerical solution to a wide range of nonlinear wave equations. The methods combine Adams-Bashforth and Adams-Moulton methods for the nonlinear and stiff linear parts, respectively, with the novel feature that different methods are used in different wavenumber ranges. The result combines high temporal accuracy with good stability properties. Numerical tests conducted on the Korteweg-de Vries and nonlinear Schrödinger equations show that the new approach is computationally more effective than other currently available methods.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 1384948
zbMATH Keywords: spectral method
zbMATH Keywords: numerical examples
zbMATH Keywords: linear dispersion
zbMATH Keywords: nonlinear wave equations
zbMATH Keywords: Adams-Bashforth and Adams-Moulton methods
zbMATH Keywords: stability
reviewed by: Qin Meng Zhao
describes a project that uses: RODAS
MaRDI profile type: Publication
OpenAlex ID: W1995277785
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DOI: 10.1006/JCPH.1999.6351
description: scientific article; zbMATH DE number 1384948