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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/50660

Title: The method of particular solutions for solving axisymmetric polyharmonic and poly-Helmholtz equations
Authors: Chia-Cheng Tsai
C.S.Chen
Tai-Wen Hsu
Contributors: 國立臺灣海洋大學:河海工程學系
Keywords: Particular solution
Method of fundamental solutions
Axisymmetric polyharmonic operator
Axisymmetric poly-Helmholtz operator
Chebyshev polynomial
Meshless methods
Date: 2009-12
Issue Date: 2018-10-19T08:20:15Z
Publisher: Engineering Analysis with Boundary Elements
Abstract: Abstract: 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.
Relation: 33(12) pp.1396-1402
URI: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/50660
Appears in Collections:[河海工程學系] 期刊論文

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