A Revisit on the Derivation of the Particular Solution for the Differential Operator ∆<sup>2</sup> ± λ<sup>2</sup>
Year: 2009
Author: Guangming Yao, C. S. Chen, Chia Cheng Tsai
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 6 : pp. 750–768
Abstract
In this paper, we applied the polyharmonic splines as the basis functions to derive particular solutions for the differential operator ∆2 ± λ2. Similar to the derivation of fundamental solutions, it is non-trivial to derive particular solutions for higher order differential operators. In this paper, we provide a simple algebraic factorization approach to derive particular solutions for these types of differential operators in 2D and 3D. The main focus of this paper is its simplicity in the sense that minimal mathematical background is required for numerically solving higher order partial differential equations such as thin plate vibration. Three numerical examples in both 2D and 3D are given to validate particular solutions we derived.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.09-m09S01
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 6 : pp. 750–768
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: The method of fundamental solutions radial basis functions meshless methods polyharmonic splines the method of particular solutions.
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