@Article{AAMM-12-1113, author = {Li , WenRubasinghe , KalaniYao , Guangming and H. Kuo , L.}, 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 = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0033}, url = {http://global-sci.org/intro/article_detail/aamm/17742.html} }