A numerical solution for Hirota-Satsuma coupled KdV equation
type: Item
instance of: scholarly article
title: A numerical solution for Hirota-Satsuma coupled KdV equation
zbMATH Open document ID: 1474.65388
DOI: 10.1155/2014/819367
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: A Petrov-Galerkin method and product approximation technique are used to solve numerically the Hirota-Satsuma coupled Korteweg-de Vries equation, using cubic \(B\)-splines as test functions and a linear \(B\)-spline as trial functions. The implicit midpoint rule is used to advance the solution in time. Newton's method is used to solve the block nonlinear pentadiagonal system we have obtained. The resulting schemes are of second order accuracy in both directions, space and time. The von Neumann stability analysis of the schemes shows that the two schemes are unconditionally stable. The single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitons, three solitons, and birth of solitons is also discussed.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 7023139
Wikidata QID: Q59041781
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/819367
OpenAlex ID: W1967400749
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description: scientific article; zbMATH DE number 7023139