Petrov-Galerkin method for the coupled Schrödinger-KdV equation
type: Item
instance of: scholarly article
title: Petrov-Galerkin method for the coupled Schrödinger-KdV equation
zbMATH Open document ID: 1474.65353
DOI: 10.1155/2014/705204
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Petrov-Galerkin method is used to derive a numerical scheme for the coupled Schrödinger-KdV (SKdV) equations, where we have used the cubic B-splines as a test functions and a linear B-splines as a trial functions. Product approximation technique is used to deal with the nonlinear terms. An implicit midpoint rule and the Runge-Kutta method of fourth-order (RK4) are used to discretize in time. A block nonlinear pentadiagonal system is obtained. We solve this system by the fixed point method. The resulting scheme has a fourth-order accuracy in space direction and second-order in time direction in case of the implicit midpoint rule and it is unconditionally stable by von Neumann method. Using the RK4 method the scheme will be linear and fourth-order in time and space directions, and it is also conditionally stable. The exact soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness and the efficiency of the proposed schemes.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 7022911
Wikidata QID: Q59040749
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/705204
OpenAlex ID: W2171201183
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description: scientific article; zbMATH DE number 7022911