The Modified Localized Method of Approximated Particular Solutions for Linear and Nonlinear Convection-Diffusion-Reaction PDEs
Year: 2020
Author: Wen Li, Kalani Rubasinghe, Guangming Yao, L. H. Kuo
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 5 : pp. 1113–1136
Abstract
In this paper, a kernel based method, the modified localized method of approximated particular solutions (MLMAPS) [16, 23] is utilized to solve unsteady-state linear and nonlinear diffusion-reaction PDEs with or without convections. The time-space and spatial space are discretized by the higher-order Houbolt method with various time step sizes and the MLMAPS, respectively. The local truncation error associated with the time discretization is $\mathcal{O}(h^4)$, where $h$ is the largest time step size used. The spatial domain is then treated by a special kernel, the integrated polyharmonic splines kernels together with low-order polynomial basis. Typical computational algorithms require a trade off between accuracy and rate of convergency. However, the experimental analysis has shown high accuracy and fast convergence of the proposed method.
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-2019-0033
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 5 : pp. 1113–1136
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Polyharmonic spline Houbolt method time-dependent PDEs method of approximated particular solutions MLMAPS convection-diffusion-reaction nonlinear kernel methods.
Author Details
-
A meshless collocation method with a global refinement strategy for reaction-diffusion systems on evolving domains
Li, Siqing
Qiao, Zhonghua
Discrete & Continuous Dynamical Systems - B, Vol. 27 (2022), Iss. 1 P.601
https://doi.org/10.3934/dcdsb.2021057 [Citations: 1]