A comparison of Fourier pseudospectral methods for the solution of the Korteweg-de Vries equation
type: Item
instance of: scholarly article
title: A comparison of Fourier pseudospectral methods for the solution of the Korteweg-de Vries equation
zbMATH Open document ID: 0683.65103
DOI: 10.1016/0021-9991(89)90122-8
author: F. Z. Nouri
author: David Sloan
published in: Journal of Computational Physics
publication date: 1989-01-01T00:00:00Z
review text: The paper deals with some numerical approaches to obtain a solution of the Korteweg-de Vries equation \(u_ t+6uu_ x+u_{xxx}=0\) over a time interval from \(t=0\) to \(t=T\) with initial conditions which match the analytic 1-soliton and 2-soliton solutions. The authors use various methods, and for an efficiency comparison the maximum acceptable point- wise error at \(t=T\) is specified and the parameters such as time-step are adjusted to minimize the computing time subject to this error constraint. Pseudospectral methods are also compared from an accuracy viewpoint by investigating how capable they are of reproducing the recurrence phenomenon described by \textit{N. J. Zabusky} and \textit{M. D. Kruskal} [Phys. Rev. Lett. 15, 240 (1965)].
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4119570
zbMATH Keywords: soliton solution
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: efficiency comparison
zbMATH Keywords: error constraint
zbMATH Keywords: Pseudospectral methods
zbMATH Keywords: recurrence phenomenon
Wikidata QID: Q57761917
MaRDI profile type: Publication
full work available at URL: 0021-9991(89)90122-8
OpenAlex ID: W2021048419
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description: scientific article; zbMATH DE number 4119570