Numerical Treatment of the Modified Time Fractional Fokker-Planck Equation
A numerical method for the modified time fractional Fokker-Planck equation is proposed. Stability and convergence of the method are rigorously discussed by means of the Fourier method. We prove that the difference scheme is unconditionally stable, and convergence order is O(τ+h4), where τ and h are...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/282190 |
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| _version_ | 1832550010074431488 |
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| author | Yuxin Zhang |
| author_facet | Yuxin Zhang |
| author_sort | Yuxin Zhang |
| collection | DOAJ |
| description | A numerical method for the modified time fractional Fokker-Planck equation is proposed. Stability and convergence of the method are
rigorously discussed by means of the Fourier method. We prove that the difference
scheme is unconditionally stable, and convergence order is O(τ+h4), where τ and h are the temporal and spatial step sizes, respectively. Finally, numerical results are given to confirm the theoretical analysis. |
| format | Article |
| id | doaj-art-83dbe990e7aa417da06f3b76efd9da55 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-83dbe990e7aa417da06f3b76efd9da552025-02-03T06:07:59ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/282190282190Numerical Treatment of the Modified Time Fractional Fokker-Planck EquationYuxin Zhang0School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, ChinaA numerical method for the modified time fractional Fokker-Planck equation is proposed. Stability and convergence of the method are rigorously discussed by means of the Fourier method. We prove that the difference scheme is unconditionally stable, and convergence order is O(τ+h4), where τ and h are the temporal and spatial step sizes, respectively. Finally, numerical results are given to confirm the theoretical analysis.http://dx.doi.org/10.1155/2014/282190 |
| spellingShingle | Yuxin Zhang Numerical Treatment of the Modified Time Fractional Fokker-Planck Equation Abstract and Applied Analysis |
| title | Numerical Treatment of the Modified Time Fractional Fokker-Planck Equation |
| title_full | Numerical Treatment of the Modified Time Fractional Fokker-Planck Equation |
| title_fullStr | Numerical Treatment of the Modified Time Fractional Fokker-Planck Equation |
| title_full_unstemmed | Numerical Treatment of the Modified Time Fractional Fokker-Planck Equation |
| title_short | Numerical Treatment of the Modified Time Fractional Fokker-Planck Equation |
| title_sort | numerical treatment of the modified time fractional fokker planck equation |
| url | http://dx.doi.org/10.1155/2014/282190 |
| work_keys_str_mv | AT yuxinzhang numericaltreatmentofthemodifiedtimefractionalfokkerplanckequation |