http://scholars.ntou.edu.tw/handle/123456789/20879
標題: | The method of particular solutions for solving axisymmetric polyharmonic and poly-Helmholtz equations | 作者: | Chia-Cheng Tsai C.S. Chen Tai-Wen Hsu |
關鍵字: | Particular solution;Method of fundamental solutions;Axisymmetric polyharmonic operator;Chebyshev polynomial | 公開日期: | 十二月-2009 | 卷: | 33 | 期: | 12 | 起(迄)頁: | 1396–1402 | 來源出版物: | Engineering Analysis with Boundary Elements | 摘要: | In this paper we derive analytical particular solutions for the axisymmetric polyharmonic and poly-Helmholtz partial differential operators using Chebyshev polynomials as basis functions. We further extend the proposed approach to the particular solutions of the product of Helmholtz-type operators. By using this formulation, we can approximate the particular solution when the forcing term of the differential equation is approximated by a truncated series of Chebyshev polynomials. These formulas were further implemented to solve inhomogeneous partial differential equations (PDEs) in which the homogeneous solutions were obtained by the method of fundamental solutions (MFS). Several numerical experiments were carried out to validate our newly derived particular solutions. Due to the exponential convergence of Chebyshev interpolation and the MFS, our numerical results are extremely accurate. |
URI: | http://scholars.ntou.edu.tw/handle/123456789/20879 | ISSN: | 0955-7997 | DOI: | 10.1016/j.enganabound.2009.04.013 |
顯示於: | 河海工程學系 海洋工程科技學士學位學程(系) |
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