@Article{AAMM-12-5,
author = {Wen, Li and Rubasinghe, Kalani and Yao, Guangming and L., Kuo, H.},
title = {The Modified Localized Method of Approximated Particular Solutions for Linear and Nonlinear Convection-Diffusion-Reaction PDEs},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2020},
volume = {12},
number = {5},
pages = {1113--1136},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2019-0033},
url = {https://global-sci.com/article/73070/the-modified-localized-method-of-approximated-particular-solutions-for-linear-and-nonlinear-convection-diffusion-reaction-pdes}
}