arrow
Volume 12, Issue 5
The Modified Localized Method of Approximated Particular Solutions for Linear and Nonlinear Convection-Diffusion-Reaction PDEs

Wen Li, Kalani Rubasinghe, Guangming Yao & L. H. Kuo

Adv. Appl. Math. Mech., 12 (2020), pp. 1113-1136.

Published online: 2020-07

Export citation
  • 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.

  • Keywords

Polyharmonic spline, Houbolt method, time-dependent PDEs, method of approximated particular solutions, MLMAPS, convection-diffusion-reaction, nonlinear, kernel methods.

  • AMS Subject Headings

65N35, 65N99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-12-1113, author = {Wen and Li and and 8321 and and Wen Li and Kalani and Rubasinghe and and 8322 and and Kalani Rubasinghe and Guangming and Yao and and 8323 and and Guangming Yao and L. and H. Kuo and and 8324 and and L. H. Kuo}, 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} }
TY - JOUR T1 - The Modified Localized Method of Approximated Particular Solutions for Linear and Nonlinear Convection-Diffusion-Reaction PDEs AU - Li , Wen AU - Rubasinghe , Kalani AU - Yao , Guangming AU - H. Kuo , L. JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1113 EP - 1136 PY - 2020 DA - 2020/07 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0033 UR - https://global-sci.org/intro/article_detail/aamm/17742.html KW - Polyharmonic spline, Houbolt method, time-dependent PDEs, method of approximated particular solutions, MLMAPS, convection-diffusion-reaction, nonlinear, kernel methods. AB -

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.

Wen Li, Kalani Rubasinghe, Guangming Yao & L. H. Kuo. (2020). The Modified Localized Method of Approximated Particular Solutions for Linear and Nonlinear Convection-Diffusion-Reaction PDEs. Advances in Applied Mathematics and Mechanics. 12 (5). 1113-1136. doi:10.4208/aamm.OA-2019-0033
Copy to clipboard
The citation has been copied to your clipboard