A fast time stepping Legendre spectral method for solving fractional Cable equation with smooth and non-smooth solutions
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144302656. Available under License Creative Commons Attribution Non-commercial No Derivatives 2.5. |
Description
To improve the calculation accuracy and efficiency, in this article, we develop a fast time stepping Legendre spectral method for solving fractional Cable equation, where in temporal direction the time stepping method is utilized and the spatial variable is discretized by Legendre spectral method. The time stepping method is used to approximate fractional order derivative, and its convergence accuracy in time is O(τ2). The fast algorithm is applied to the time stepping method and it can reduce the computational complexity from O(M2) to O(MlogM), where M denotes the number of time stepping. For non-smooth solutions, we deal with the initial singularity by adding correction terms. We also analyze the numerical stability and convergence in detail. Numerical experiments confirm our theoretical analysis and efficiency of the fast algorithm.
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| ID Code: | 243097 | ||
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| Item Type: | Contribution to Journal (Journal Article) | ||
| Refereed: | Yes | ||
| ORCID iD: |
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| Additional Information: | Funding Information: This work is supported by National Natural Science Foundation of China (Nos. 11801060 ). | ||
| Measurements or Duration: | 17 pages | ||
| Keywords: | Fast algorithm, Legendre spectral method, Smooth and non-smooth solutions, Stability and convergence, Time stepping method | ||
| DOI: | 10.1016/j.matcom.2023.04.009 | ||
| ISSN: | 0378-4754 | ||
| Pure ID: | 144302656 | ||
| Divisions: | Current > QUT Faculties and Divisions > Faculty of Science Current > Schools > School of Mathematical Sciences |
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| Funding Information: | This work is supported by National Natural Science Foundation of China (Nos. 11801060 ). | ||
| Copyright Owner: | 2023 International Association for Mathematics and Computers in Simulation (IMACS) | ||
| Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||
| Deposited On: | 20 Sep 2023 05:47 | ||
| Last Modified: | 03 Aug 2024 00:45 |
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