A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation
Abstract The fractional reaction–diffusion equation has profound physical and engineering background, and its rapid solution research is of important scientific significance and engineering application value. In this paper, we propose a parallel computing method of mixed difference scheme for time f...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2345-4 |
| _version_ | 1818534548508508160 |
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| author | Xiaozhong Yang Xu Dang |
| author_facet | Xiaozhong Yang Xu Dang |
| author_sort | Xiaozhong Yang |
| collection | DOAJ |
| description | Abstract The fractional reaction–diffusion equation has profound physical and engineering background, and its rapid solution research is of important scientific significance and engineering application value. In this paper, we propose a parallel computing method of mixed difference scheme for time fractional reaction–diffusion equation and construct a class of improved alternating segment Crank–Nicolson (IASC–N) difference schemes. The class of parallel difference schemes constructed in this paper, based on the classical Crank–Nicolson (C–N) scheme and classical explicit and implicit schemes, combines with alternating segment techniques. We illustrate the unique existence, unconditional stability, and convergence of the parallel difference scheme solution theoretically. Numerical experiments verify the theoretical analysis, which shows that the IASC–N scheme has second order spatial accuracy and 2−α $2-\alpha $ order temporal accuracy, and the computational efficiency is greatly improved compared with the implicit scheme and C–N scheme. The IASC–N scheme has ideal computation accuracy and obvious parallel computing properties, showing that the IASC–N parallel difference method is effective for solving time fractional reaction–diffusion equation. |
| first_indexed | 2024-12-11T18:13:04Z |
| format | Article |
| id | doaj.art-efc8dc3baf6c4c999c24205618f1209b |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T18:13:04Z |
| publishDate | 2019-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-efc8dc3baf6c4c999c24205618f1209b2022-12-22T00:55:30ZengSpringerOpenAdvances in Difference Equations1687-18472019-10-012019111810.1186/s13662-019-2345-4A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equationXiaozhong Yang0Xu Dang1School of Mathematics and Physics, North China Electric Power UniversitySchool of Mathematics and Physics, North China Electric Power UniversityAbstract The fractional reaction–diffusion equation has profound physical and engineering background, and its rapid solution research is of important scientific significance and engineering application value. In this paper, we propose a parallel computing method of mixed difference scheme for time fractional reaction–diffusion equation and construct a class of improved alternating segment Crank–Nicolson (IASC–N) difference schemes. The class of parallel difference schemes constructed in this paper, based on the classical Crank–Nicolson (C–N) scheme and classical explicit and implicit schemes, combines with alternating segment techniques. We illustrate the unique existence, unconditional stability, and convergence of the parallel difference scheme solution theoretically. Numerical experiments verify the theoretical analysis, which shows that the IASC–N scheme has second order spatial accuracy and 2−α $2-\alpha $ order temporal accuracy, and the computational efficiency is greatly improved compared with the implicit scheme and C–N scheme. The IASC–N scheme has ideal computation accuracy and obvious parallel computing properties, showing that the IASC–N parallel difference method is effective for solving time fractional reaction–diffusion equation.http://link.springer.com/article/10.1186/s13662-019-2345-4Fractional reaction–diffusion equationIASC–N difference schemeUnconditional stabilityOrder of convergenceParallel computing |
| spellingShingle | Xiaozhong Yang Xu Dang A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation Advances in Difference Equations Fractional reaction–diffusion equation IASC–N difference scheme Unconditional stability Order of convergence Parallel computing |
| title | A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation |
| title_full | A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation |
| title_fullStr | A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation |
| title_full_unstemmed | A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation |
| title_short | A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation |
| title_sort | new parallel difference algorithm based on improved alternating segment crank nicolson scheme for time fractional reaction diffusion equation |
| topic | Fractional reaction–diffusion equation IASC–N difference scheme Unconditional stability Order of convergence Parallel computing |
| url | http://link.springer.com/article/10.1186/s13662-019-2345-4 |
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