Polynomial Particular Solutions for Solving Elliptic Partial Differential Equations

Authors

Thir R. Dangal, University of Southern MississippiFollow
Ching-Shyang Chen, University of Southern MississippiFollow
Ji Lin, Hohai UniversityFollow

Document Type

Article

Publication Date

1-1-2017

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

In the past, polynomial particular solutions have been obtained for certain types of partial differential operators without convection terms. In this paper, a closed-form particular solution for more general partial differential operators with constant coefficients has been derived for polynomial basis functions. The newly derived particular solution is further coupled with the method of particular solutions (MPS) for numerically solving a large class of elliptic partial differential equations. In contrast to the use of Chebyshev polynomial basis functions, the proposed approach is more flexible in selecting the collocation points inside the domain. The polynomial basis functions are well-known for yielding ill-conditioned systems when their order becomes large. The multiple scale technique is applied to circumvent the difficulty of ill-conditioning problem. Five numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.

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/.

Publication Title

Computers & Mathematics with Applications

Volume

73

Issue

1

First Page

60

Last Page

70

Recommended Citation

Dangal, T. R., Chen, C., Lin, J. (2017). Polynomial Particular Solutions for Solving Elliptic Partial Differential Equations. Computers & Mathematics with Applications, 73(1), 60-70.
Available at: https://aquila.usm.edu/fac_pubs/15309