An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations

doi:10.1088/1674-1056/22/10/100204

Abstract The present paper deals with the numerical solution of the coupled Schrödinger-KdV equations using the element-free Galerkin (EFG) method which is based on the moving least-square approximation. Instead of traditional mesh oriented methods such as the finite difference method (FDM) and the finite element method (FEM), this method needs only scattered nodes in the domain. For this scheme, a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method. In numerical experiments, the results are presented and compared with the findings of the finite element method, the radial basis functions method, and an analytical solution to confirm the good accuracy of the presented scheme.

Keywords: element-free Galerkin (EFG) method meshless method the coupled Schrö dinger-KdV equations

Received: 19 October 2012
Revised: 07 April 2013
Accepted manuscript online:

PACS:	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)
	03.65.Ge	(Solutions of wave equations: bound states)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11072117 and 61074142), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110007), Scientific Research Fund of Zhejiang Provincial Education Department, China (Grant No. Z201119278), the Natural Science Foundation of Ningbo City (Grant Nos. 2012A610152 and 2012A610038), the Disciplinary Project of Ningbo City, China (Grant No. SZXL1067), and K. C. Wong Magna Fund in Ningbo University.

Corresponding Authors: Ge Hong-Xia
E-mail: gehongxia@nbu.edu.cn

Cite this article:

Liu Yong-Qing (刘永庆), Cheng Rong-Jun (程荣军), Ge Hong-Xia (葛红霞) An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations 2013 Chin. Phys. B 22 100204

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An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations

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