Crank-Nicolson finite difference method for two-dimensional fractional sub-diffusion equation
A Crank-Nicolson finite difference method is presented to solve the time fractional two-dimensional sub-diffusion equation in the case where the Gr¨unwald-Letnikov definition is used for the time-fractional derivative. The stability and convergence of the proposed Crank-Nicolson scheme are also an...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
International Scientific Publications and Consulting Services (ISPACS)
2017
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| Subjects: | |
| Online Access: | http://eprints.usm.my/38542/ http://eprints.usm.my/38542/1/Crank-Nicolson_finite_difference_method_for_two-dimensional_fractional_sub-diffusion_equation.pdf |
| _version_ | 1848878498860498944 |
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| author | Ali, Umair Abdullah, Farah Aini Ismail, Ahmad Izani |
| author_facet | Ali, Umair Abdullah, Farah Aini Ismail, Ahmad Izani |
| author_sort | Ali, Umair |
| building | USM Institutional Repository |
| collection | Online Access |
| description | A Crank-Nicolson finite difference method is presented to solve the time fractional two-dimensional sub-diffusion
equation in the case where the Gr¨unwald-Letnikov definition is used for the time-fractional derivative. The stability
and convergence of the proposed Crank-Nicolson scheme are also analyzed. Finally, numerical examples are presented
to test that the numerical scheme is accurate and feasible. |
| first_indexed | 2025-11-15T17:32:18Z |
| format | Article |
| id | usm-38542 |
| institution | Universiti Sains Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T17:32:18Z |
| publishDate | 2017 |
| publisher | International Scientific Publications and Consulting Services (ISPACS) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | usm-385422018-01-25T06:50:58Z http://eprints.usm.my/38542/ Crank-Nicolson finite difference method for two-dimensional fractional sub-diffusion equation Ali, Umair Abdullah, Farah Aini Ismail, Ahmad Izani QA1-939 Mathematics A Crank-Nicolson finite difference method is presented to solve the time fractional two-dimensional sub-diffusion equation in the case where the Gr¨unwald-Letnikov definition is used for the time-fractional derivative. The stability and convergence of the proposed Crank-Nicolson scheme are also analyzed. Finally, numerical examples are presented to test that the numerical scheme is accurate and feasible. International Scientific Publications and Consulting Services (ISPACS) 2017 Article PeerReviewed application/pdf en http://eprints.usm.my/38542/1/Crank-Nicolson_finite_difference_method_for_two-dimensional_fractional_sub-diffusion_equation.pdf Ali, Umair and Abdullah, Farah Aini and Ismail, Ahmad Izani (2017) Crank-Nicolson finite difference method for two-dimensional fractional sub-diffusion equation. Journal of Interpolation and Approximation in Scientific Computing, 2017 (2). pp. 18-29. ISSN 2194-3907 https://doi.org/10.5899/2017/jiasc-00117 |
| spellingShingle | QA1-939 Mathematics Ali, Umair Abdullah, Farah Aini Ismail, Ahmad Izani Crank-Nicolson finite difference method for two-dimensional fractional sub-diffusion equation |
| title | Crank-Nicolson finite difference method for two-dimensional
fractional sub-diffusion equation |
| title_full | Crank-Nicolson finite difference method for two-dimensional
fractional sub-diffusion equation |
| title_fullStr | Crank-Nicolson finite difference method for two-dimensional
fractional sub-diffusion equation |
| title_full_unstemmed | Crank-Nicolson finite difference method for two-dimensional
fractional sub-diffusion equation |
| title_short | Crank-Nicolson finite difference method for two-dimensional
fractional sub-diffusion equation |
| title_sort | crank-nicolson finite difference method for two-dimensional
fractional sub-diffusion equation |
| topic | QA1-939 Mathematics |
| url | http://eprints.usm.my/38542/ http://eprints.usm.my/38542/ http://eprints.usm.my/38542/1/Crank-Nicolson_finite_difference_method_for_two-dimensional_fractional_sub-diffusion_equation.pdf |