Volume 12, Issue 1
A Support Vector Machine Method for Two Time-Scale Variable-Order Time-Fractional Diffusion Equations

Zhiwei Yang, Huan Liu, Xu Guo & Hong Wang

East Asian J. Appl. Math., 12 (2022), pp. 145-162.

Published online: 2021-10

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  • Abstract

An efficient least-square support vector machine (LS-SVM) method for a two time-scale variable-order time-fractional diffusion equation is developed. The method is particularly suitable for problems defined on complex physical domains or in high spatial dimensions. The problem is discretised by the L1 scheme and the Euler method. The temporal semi-discrete problem obtained is reformulated as a minimisation problem. The Karush-Kuhn-Tucker optimality condition is used to determine the minimiser of the optimisation problem and, hence, the solution sought. Numerical experiments show the efficiency and high accuracy of the method.

  • Keywords

Least-square support vector machine, variable-order, time-fractional diffusion equation, irregular domain.

  • AMS Subject Headings

65M22, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-145, author = {Yang , Zhiwei and Liu , Huan and Guo , Xu and Wang , Hong}, title = {A Support Vector Machine Method for Two Time-Scale Variable-Order Time-Fractional Diffusion Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {12}, number = {1}, pages = {145--162}, abstract = {

An efficient least-square support vector machine (LS-SVM) method for a two time-scale variable-order time-fractional diffusion equation is developed. The method is particularly suitable for problems defined on complex physical domains or in high spatial dimensions. The problem is discretised by the L1 scheme and the Euler method. The temporal semi-discrete problem obtained is reformulated as a minimisation problem. The Karush-Kuhn-Tucker optimality condition is used to determine the minimiser of the optimisation problem and, hence, the solution sought. Numerical experiments show the efficiency and high accuracy of the method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.310121.120821}, url = {http://global-sci.org/intro/article_detail/eajam/19925.html} }
TY - JOUR T1 - A Support Vector Machine Method for Two Time-Scale Variable-Order Time-Fractional Diffusion Equations AU - Yang , Zhiwei AU - Liu , Huan AU - Guo , Xu AU - Wang , Hong JO - East Asian Journal on Applied Mathematics VL - 1 SP - 145 EP - 162 PY - 2021 DA - 2021/10 SN - 12 DO - http://doi.org/10.4208/eajam.310121.120821 UR - https://global-sci.org/intro/article_detail/eajam/19925.html KW - Least-square support vector machine, variable-order, time-fractional diffusion equation, irregular domain. AB -

An efficient least-square support vector machine (LS-SVM) method for a two time-scale variable-order time-fractional diffusion equation is developed. The method is particularly suitable for problems defined on complex physical domains or in high spatial dimensions. The problem is discretised by the L1 scheme and the Euler method. The temporal semi-discrete problem obtained is reformulated as a minimisation problem. The Karush-Kuhn-Tucker optimality condition is used to determine the minimiser of the optimisation problem and, hence, the solution sought. Numerical experiments show the efficiency and high accuracy of the method.

Zhiwei Yang, Huan Liu, Xu Guo & Hong Wang. (2021). A Support Vector Machine Method for Two Time-Scale Variable-Order Time-Fractional Diffusion Equations. East Asian Journal on Applied Mathematics. 12 (1). 145-162. doi:10.4208/eajam.310121.120821
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