Document Type
Article
Publication Date
6-2018
Department
Mathematics
School
Mathematics and Natural Sciences
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.
Publication Title
Journal of Computational and Applied Mathematics
Volume
335
First Page
20
Last Page
32
Recommended Citation
Tian, Z.,
Li, X.,
Fan, C.,
Chen, C.
(2018). The Method of Particular Solutions Using Trigonometric Basis Functions. Journal of Computational and Applied Mathematics, 335, 20-32.
Available at: https://aquila.usm.edu/fac_pubs/14925
Comments
© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/.