Journal
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
Volume 108, Issue -, Pages 95-107Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.enganabound.2019.08.018
Keywords
Sine-Gordon equation; Generalized thin plate splines (GTPS); Radial basis functions (RBFs); Localized method of approximate particular solutions (LMAPS); Numerical solution
Funding
- Russian Federation Government [Y26.31.0013]
- RFBR [17-01-00689]
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Sine-Gordon equation is one of the most famous nonlinear hyperbolic partial differential equations, it arises in many science and engineering fields. In the present work, we consider the numerical solution of two dimensional sine-Gordon equation using localized method of approximate particular solutions (LMAPS), in this technique, the method of approximate particular solutions (MAPS) occurs on some local domains, that greatly reduces the size of the collection matrix, and by combining the conditional positive radial basis function (RBF) generalized thin plate splines (GTPS) with additional low-order polynomial basis to avoid selecting shape parameters during localization. This method is effective compared with other existing methods and since this method is really meshless, it can be used to solve the nonlinear model with complicated computational domains. Several numerical examples are given to demonstrate the ability and accuracy of the present approach for solving nonlinear sine-Gordon equation.
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