An Efficient Method of Approximate Particular Solutions Using Polynomial Basis Functions

Authors

Cheng Deng, Nanchang University
Hui Zheng, Nanchang University
Mingfu Fu, Nanchang University
Jingang Xiong, Nanchang University
C. S. Chen, Nanchang UniversityFollow

Document Type

Article

Publication Date

2-1-2020

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

© 2019 Elsevier Ltd The most challenging task of the method of approximate particular solutions (MAPS) is the generation of the closed-form particular solutions with respect to the given differential operator using various basis functions. These particular solutions have to be generated prior to the solution process of the partial differential equations. In this paper, we propose a different approach without the tedious and inefficient solution procedure using symbolic computation to produce the closed-form particular solutions. The proposed approach is introduced and extended to solve a large class of elliptic partial differential equations (PDEs) based on the method of approximate particular solutions (MAPS). Numerical results show the proposed approach is simple, efficient, accurate, and stable. Five different numerical examples are presented to demonstrate the effectiveness of the proposed method.

Publication Title

Engineering Analysis with Boundary Elements

Volume

111

First Page

1

Last Page

8

Recommended Citation

Deng, C., Zheng, H., Fu, M., Xiong, J., Chen, C. (2020). An Efficient Method of Approximate Particular Solutions Using Polynomial Basis Functions. Engineering Analysis with Boundary Elements, 111, 1-8.
Available at: https://aquila.usm.edu/fac_pubs/17878