An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations
In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A numerical scheme for the equation has been derived to obtain 2-α in time and fourth-order in space. We improve the results by constructing a compact scheme of second-o...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/3263589 |
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| author | Lei Ren Lei Liu |
| author_facet | Lei Ren Lei Liu |
| author_sort | Lei Ren |
| collection | DOAJ |
| description | In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A numerical scheme for the equation has been derived to obtain 2-α in time and fourth-order in space. We improve the results by constructing a compact scheme of second-order in time while keeping fourth-order in space. Based on the L2-1σ approximation formula and a fourth-order compact finite difference approximation, the stability of the constructed scheme and its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Applications using two model problems demonstrate the theoretical results. |
| format | Article |
| id | doaj-art-af930973cbd5453fb4530429f5652060 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-af930973cbd5453fb4530429f56520602025-02-03T01:28:56ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/32635893263589An Efficient Compact Difference Method for Temporal Fractional Subdiffusion EquationsLei Ren0Lei Liu1School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, ChinaSchool of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, ChinaIn this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A numerical scheme for the equation has been derived to obtain 2-α in time and fourth-order in space. We improve the results by constructing a compact scheme of second-order in time while keeping fourth-order in space. Based on the L2-1σ approximation formula and a fourth-order compact finite difference approximation, the stability of the constructed scheme and its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Applications using two model problems demonstrate the theoretical results.http://dx.doi.org/10.1155/2019/3263589 |
| spellingShingle | Lei Ren Lei Liu An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations Advances in Mathematical Physics |
| title | An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations |
| title_full | An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations |
| title_fullStr | An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations |
| title_full_unstemmed | An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations |
| title_short | An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations |
| title_sort | efficient compact difference method for temporal fractional subdiffusion equations |
| url | http://dx.doi.org/10.1155/2019/3263589 |
| work_keys_str_mv | AT leiren anefficientcompactdifferencemethodfortemporalfractionalsubdiffusionequations AT leiliu anefficientcompactdifferencemethodfortemporalfractionalsubdiffusionequations AT leiren efficientcompactdifferencemethodfortemporalfractionalsubdiffusionequations AT leiliu efficientcompactdifferencemethodfortemporalfractionalsubdiffusionequations |