An efficient method of approximate particular solutions using polynomial basis functions. (February 2020)

• Record Type: Journal Article
• Authors: Deng, Cheng; Zheng, Hui; Fu, Mingfu; Xiong, Jingang; Chen, C.S.
• Is Part Of: Engineering analysis with boundary elements. Volume 111(2020)
• Page Start: 1
• Page End: 8
• Publication Date: 2020-02
• Subjects: Method of approximate particular solutions -- Helmholtz-type equation -- Polynomial basis functions -- Multiple scale technique; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2019.10.014
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: 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.