Generalized Alikhanov's approximation and numerical treatment of generalized fractional sub-diffusion equations
In this paper, we develop a new approximation for the generalized fractional derivative, which is characterized by a scale function and a weight function. The new approximation is then used in the numerical treatment of a class of generalized fractional sub-diffusion equations. The theoretical aspec...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Online Access: | https://hdl.handle.net/10356/160563 |
| _version_ | 1811692678141706240 |
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| author | Li, Xuhao Wong, Patricia Jia Yiing |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Li, Xuhao Wong, Patricia Jia Yiing |
| author_sort | Li, Xuhao |
| collection | NTU |
| description | In this paper, we develop a new approximation for the generalized fractional derivative, which is characterized by a scale function and a weight function. The new approximation is then used in the numerical treatment of a class of generalized fractional sub-diffusion equations. The theoretical aspects of solvability, stability and convergence are established rigorously in maximum norm by discrete energy methodology. Due to the new approximation, the theoretical temporal convergence order of the numerical scheme improves those of earlier work. To confirm, four examples are presented to illustrate the accuracy of the proposed scheme and to compare with other methods in the literature. |
| first_indexed | 2024-10-01T06:39:36Z |
| format | Journal Article |
| id | ntu-10356/160563 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:39:36Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1605632022-07-26T08:40:49Z Generalized Alikhanov's approximation and numerical treatment of generalized fractional sub-diffusion equations Li, Xuhao Wong, Patricia Jia Yiing School of Electrical and Electronic Engineering Science::Mathematics Generalized Fractional Derivative Numerical Scheme In this paper, we develop a new approximation for the generalized fractional derivative, which is characterized by a scale function and a weight function. The new approximation is then used in the numerical treatment of a class of generalized fractional sub-diffusion equations. The theoretical aspects of solvability, stability and convergence are established rigorously in maximum norm by discrete energy methodology. Due to the new approximation, the theoretical temporal convergence order of the numerical scheme improves those of earlier work. To confirm, four examples are presented to illustrate the accuracy of the proposed scheme and to compare with other methods in the literature. 2022-07-26T08:40:49Z 2022-07-26T08:40:49Z 2021 Journal Article Li, X. & Wong, P. J. Y. (2021). Generalized Alikhanov's approximation and numerical treatment of generalized fractional sub-diffusion equations. Communications in Nonlinear Science and Numerical Simulation, 97, 105719-. https://dx.doi.org/10.1016/j.cnsns.2021.105719 1007-5704 https://hdl.handle.net/10356/160563 10.1016/j.cnsns.2021.105719 2-s2.0-85100431757 97 105719 en Communications in Nonlinear Science and Numerical Simulation © 2021 Elsevier B.V. All rights reserved. |
| spellingShingle | Science::Mathematics Generalized Fractional Derivative Numerical Scheme Li, Xuhao Wong, Patricia Jia Yiing Generalized Alikhanov's approximation and numerical treatment of generalized fractional sub-diffusion equations |
| title | Generalized Alikhanov's approximation and numerical treatment of generalized fractional sub-diffusion equations |
| title_full | Generalized Alikhanov's approximation and numerical treatment of generalized fractional sub-diffusion equations |
| title_fullStr | Generalized Alikhanov's approximation and numerical treatment of generalized fractional sub-diffusion equations |
| title_full_unstemmed | Generalized Alikhanov's approximation and numerical treatment of generalized fractional sub-diffusion equations |
| title_short | Generalized Alikhanov's approximation and numerical treatment of generalized fractional sub-diffusion equations |
| title_sort | generalized alikhanov s approximation and numerical treatment of generalized fractional sub diffusion equations |
| topic | Science::Mathematics Generalized Fractional Derivative Numerical Scheme |
| url | https://hdl.handle.net/10356/160563 |
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