High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations
A high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fracti...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/642989 |
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| author | Ibrahim Karatay Serife R. Bayramoglu |
| author_facet | Ibrahim Karatay Serife R. Bayramoglu |
| author_sort | Ibrahim Karatay |
| collection | DOAJ |
| description | A high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fractional part and fourth-order accuracy compact approximation is applied for the second-order space derivative. The spectral stability and the Fourier stability analysis of the difference scheme are shown. Finally a detailed numerical analysis, including tables, figures, and error comparison, is given to demonstrate the theoretical results and high accuracy of the proposed scheme. |
| format | Article |
| id | doaj-art-e72afa5c87e14b7c927549a795814f87 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-e72afa5c87e14b7c927549a795814f872025-02-03T01:27:09ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/642989642989High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat EquationsIbrahim Karatay0Serife R. Bayramoglu1Department of Mathematics, Fatih University, 34500 Istanbul, TurkeyDepartment of Mathematics, Fatih University, 34500 Istanbul, TurkeyA high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fractional part and fourth-order accuracy compact approximation is applied for the second-order space derivative. The spectral stability and the Fourier stability analysis of the difference scheme are shown. Finally a detailed numerical analysis, including tables, figures, and error comparison, is given to demonstrate the theoretical results and high accuracy of the proposed scheme.http://dx.doi.org/10.1155/2014/642989 |
| spellingShingle | Ibrahim Karatay Serife R. Bayramoglu High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations The Scientific World Journal |
| title | High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations |
| title_full | High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations |
| title_fullStr | High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations |
| title_full_unstemmed | High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations |
| title_short | High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations |
| title_sort | high order compact difference scheme for the numerical solution of time fractional heat equations |
| url | http://dx.doi.org/10.1155/2014/642989 |
| work_keys_str_mv | AT ibrahimkaratay highordercompactdifferenceschemeforthenumericalsolutionoftimefractionalheatequations AT seriferbayramoglu highordercompactdifferenceschemeforthenumericalsolutionoftimefractionalheatequations |