A tailored finite point method for subdiffusion equation with anisotropic and discontinuous diffusivity
•This is the first attempt to construct tailored finite point method for subdiffusion equation with anisotropic and discontinuous diffusivity.•The most distinguished feature of this new scheme is that it not only can ensure high accuracy and stability for solving subdiffusion equations with high ani...
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| Published in | Applied mathematics and computation Vol. 401; p. 125907 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.07.2021
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| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2020.125907 |
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| Abstract | •This is the first attempt to construct tailored finite point method for subdiffusion equation with anisotropic and discontinuous diffusivity.•The most distinguished feature of this new scheme is that it not only can ensure high accuracy and stability for solving subdiffusion equations with high anisotropic diffusivity but also can efficiently resolve the high gradients near the side internal.•The unique solvability and unconditional stability of proposed scheme are strictly proved.
In this paper, we first propose a tailored finite point method (TFPM) for solving time fractional subdiffusion problems with anisotropic and discontinuous diffusivity. This numerical scheme can perfectly capture the rapid transition of the solutions which contain sharp interface layers even with coarse meshes. Second, the accuracy and stability of the proposed scheme are strictly analyzed. Finally, some numerical examples are provided to show the accuracy and reliability of this new scheme. |
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| AbstractList | •This is the first attempt to construct tailored finite point method for subdiffusion equation with anisotropic and discontinuous diffusivity.•The most distinguished feature of this new scheme is that it not only can ensure high accuracy and stability for solving subdiffusion equations with high anisotropic diffusivity but also can efficiently resolve the high gradients near the side internal.•The unique solvability and unconditional stability of proposed scheme are strictly proved.
In this paper, we first propose a tailored finite point method (TFPM) for solving time fractional subdiffusion problems with anisotropic and discontinuous diffusivity. This numerical scheme can perfectly capture the rapid transition of the solutions which contain sharp interface layers even with coarse meshes. Second, the accuracy and stability of the proposed scheme are strictly analyzed. Finally, some numerical examples are provided to show the accuracy and reliability of this new scheme. |
| ArticleNumber | 125907 |
| Author | Cao, Jianxiong Wang, Yihong |
| Author_xml | – sequence: 1 givenname: Yihong surname: Wang fullname: Wang, Yihong email: wyhlx2017@163.com organization: School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China – sequence: 2 givenname: Jianxiong surname: Cao fullname: Cao, Jianxiong email: caojianxiong2007@126.com organization: School of Sciences, Lanzhou University of Technology, Lanzhou 730050, China |
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| Cites_doi | 10.1016/j.jcp.2015.07.011 10.4208/cicp.2019.js60.04 10.1016/j.cam.2019.06.034 10.1016/j.jcp.2005.12.006 10.1016/S0098-3004(02)00073-0 10.1007/s10915-016-0254-1 10.1090/S0025-5718-2012-02616-0 10.1007/s10915-009-9292-2 10.1016/j.jcp.2007.02.001 10.1007/s10915-015-0152-y 10.1007/s10915-008-9187-7 10.1016/j.jcp.2014.10.018 10.1016/j.jcp.2020.109576 10.1007/s10915-017-0388-9 10.1016/j.mcm.2011.03.017 10.1016/j.apnum.2005.03.003 10.1080/00207160.2014.887702 10.1137/130934192 10.1109/TIP.2007.904971 10.1016/j.jcp.2014.09.012 10.1109/TGRS.2015.2490158 10.1016/j.camwa.2009.08.071 10.1016/j.jcp.2014.10.051 10.1016/j.jcp.2013.09.016 10.1007/s11075-015-0065-8 |
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