Adv. Appl. Math. Mech., 12 (2020), pp. 1113-1136.
Published online: 2020-07
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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} }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.