http://scholars.ntou.edu.tw/handle/123456789/1227
Title: | The method of particular solutions using trigonometric basis functions | Authors: | Zhaolu Tian Xinxiang Li C.M. Fan C.S. Chen |
Keywords: | Method of particular solutions;Trigonometric functions;Particular solution;Meshless methods;Collocation method | Issue Date: | Jun-2018 | Journal Volume: | 335 | Start page/Pages: | 20-32 | Source: | Journal of Computational and Applied Mathematics | Abstract: | In this paper, the method of particular solutions (MPS) using trigonometric functions as the basis functions is proposed to solve two-dimensional elliptic partial differential equations. The inhomogeneous term of the governing equation is approximated by Fourier series and the closed-form particular solutions of trigonometric functions are derived using the method of undetermined coefficients. Once the particular solutions for the trigonometric basis functions are derived, the standard MPS can be applied for solving partial differential equations. In comparing with the use of radial basis functions and polynomials in the MPS, our proposed approach provides another simple approach to effectively solving two-dimensional elliptic partial differential equations. Five numerical examples are provided in this paper to validate the merits of the proposed meshless method. |
URI: | http://scholars.ntou.edu.tw/handle/123456789/1227 | ISSN: | 0377-0427 | DOI: | 10.1016/j.cam.2017.11.028 |
Appears in Collections: | 河海工程學系 |
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