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

被引：10
|
作者：
Feng Zhao [1 ]
Wang Xiao-Dong [1 ]
Ouyang Jie [1 ]
机构：
[1] Northwestern Polytech Univ, Dept Appl Math, Xian 710129, Peoples R China
来源：
CHINESE PHYSICS B | 2013年 / 22卷 / 07期
关键词：
element-free Galerkin method; shifted polynomial basis; generalized fifth-order Korteweg-de Vries equation; solitary wave; MESHLESS METHODS;
D O I：
10.1088/1674-1056/22/7/074704
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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.
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页数：8
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