Year: 2020
Author: Cheng Deng, Hui Zheng, Yan Shi, C. S. Chen
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 4 : pp. 920–939
Abstract
To overcome the difficulty for solving fourth order partial differential equations (PDEs) using localized methods, we introduce and extend a recent method to decompose the particular solution of such equation into particular solutions of two second-order differential equations using radial basis functions (RBFs). In this way, the localized method of approximate particular solutions (LMAPS) can be used to directly solve a fourth-order PDE without splitting it into two second-order problems. The closed-form particular solutions for polyharmonic splines RBFs augmented with polynomial basis functions for Helmholtz-type equations are the cores of the solution process. Several novel techniques are proposed to further improve the accuracy and efficiency. Four numerical examples are presented to show the effectiveness of our approach.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0216
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 4 : pp. 920–939
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Localized method of approximate particular solutions Helmholtz-type operator fourth-order partial differential equation polynomial basis functions polyharmonic splines of RBFs.
Author Details
-
A polynomial-augmented RBF collocation method for fourth-order boundary value problems
Cao, Dingding | Li, Xinxiang | Zhu, HuiqingComputers & Mathematics with Applications, Vol. 133 (2023), Iss. P.1
https://doi.org/10.1016/j.camwa.2022.12.014 [Citations: 0] -
The local meshless method based on Pascal polynomial basis functions for solving fourth-order PDEs
Chang, Wanru | Zhang, Jianfeng | Wang, Yun | Wang, JiawenEngineering Analysis with Boundary Elements, Vol. 140 (2022), Iss. P.159
https://doi.org/10.1016/j.enganabound.2022.03.019 [Citations: 2]