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Chin. Phys. B, 2013, Vol. 22(7): 074704    DOI: 10.1088/1674-1056/22/7/074704

An improved element-free Galerkin method for solving generalized fifth-order Korteweg-de Vries equation

Feng Zhao (冯昭), Wang Xiao-Dong (王晓东), Ouyang Jie (欧阳洁)
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China
Abstract  In this paper, an improved element-free Galerkin (IEFG) method is proposed to solve the generalized fifth-order Korteweg-de Vries (gfKdV) equation. When the traditional element-free Galerkin (EFG) method is used to solve such an equation, unstable or even wrong numerical solutions may be obtained due to the violation of the consistency conditions of the moving least-squares (MLS) shape functions. To solve this problem, the EFG method is improved by employing the improved moving least-squares (IMLS) approximation based on the shifted polynomial basis functions. The effectiveness of the IEFG method for the gfKdV equation is investigated by using some numerical examples. Meanwhile, the motion of single solitary wave and the interaction of two solitons are simulated using the IEFG method.
Keywords:  element-free Galerkin method      shifted polynomial basis      generalized fifth-order Korteweg-de Vries equation      solitary wave  
Received:  11 October 2012      Revised:  08 January 2013      Accepted manuscript online: 
PACS:  47.35.Fg (Solitary waves)  
  04.30.Nk (Wave propagation and interactions)  
  02.70.Dh (Finite-element and Galerkin methods)  
  47.10.ab (Conservation laws and constitutive relations)  
Fund: Project supported by the National Basic Research Program of China (Grant No. 2012CB025903).
Corresponding Authors:  Ouyang Jie     E-mail:

Cite this article: 

Feng Zhao (冯昭), Wang Xiao-Dong (王晓东), Ouyang Jie (欧阳洁) An improved element-free Galerkin method for solving generalized fifth-order Korteweg-de Vries equation 2013 Chin. Phys. B 22 074704

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