Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 71, Issue 8, Pages 1655-1678Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2016.03.007
Keywords
Meshless; Element-free Galerkin (EFG) method; Sine-Gordon equation; Generalized sinh-Gordon equation; Soliton; Error estimate
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Funding
- National Natural Science Foundation of China [11471063, 11301575]
- Natural Science Foundation Project of CQ CSTC [cstc2014jcyjA00005]
- Program of Chongqing Innovation Team Project in University [KJTD201308]
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In this paper, a numerical scheme based on the element-free Galerkin (EFG) method is proposed to find the numerical solutions of nonlinear sine-Gordon equation with Neumann boundary condition and generalized sinh-Gordon equation with Dirichlet boundary condition. In this scheme, a time stepping technique is used to approximate the time derivative terms of the given equations. Then, the penalty method is adopted to enforce the Dirichlet boundary condition and lastly, the EFG method is performed to establish the system of discrete equations. The convergence of the proposed scheme is derived theoretically and verified numerically by doing its error analysis. Numerical examples involving line and ring solitons are given to show the accuracy and efficiency of the scheme. The numerical results are in excellent agreement with the analytical solutions and/or previously reported numerical results. (C) 2016 Elsevier Ltd. All rights reserved.
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