A high-order compact difference scheme for the multi-term time-fractional Sobolev-type convection-diffusion equation
This paper presents two high-order compact difference schemes to discuss the numerical solution of the one-dimensional and two-dimensional multi-term time-fractional convection-diffusion equation of the Sobolev type based on the Caputo fractional derivative. For this purpose, we employ the L2 formul...
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ir-123456789-298342025-03-03T09:13:10Z A high-order compact difference scheme for the multi-term time-fractional Sobolev-type convection-diffusion equation Alikhanov, A. A. Алиханов, А. А. Shahbazi Asl, M. Шахбазиасль, М. Caputo time-fractional derivative Stability and Convergence Multi-term Sobolev type equation L2 formula Compact difference scheme This paper presents two high-order compact difference schemes to discuss the numerical solution of the one-dimensional and two-dimensional multi-term time-fractional convection-diffusion equation of the Sobolev type based on the Caputo fractional derivative. For this purpose, we employ the L2 formula for the temporal discretization of the Caputo fractional derivatives and introduce a new compact difference operator for the space discretization. The proposed schemes transform the original problem into a system of algebraic equation. We present a novel analysis of the convergence and theoretical stability of both methods. The difference schemes have fourth-order and 3-max{αr,βr} order of accuracy in space and time respectively, where αr and βr are the orders of the fractional derivatives in the multi-term convection-diffusion model. Additionally, we construct an L2-type numerical scheme on non-uniform graded meshes to address problems where the solution exhibits weak initial regularity. Some test functions are provided to demonstrate the accuracy and efficiency of the proposed schemes. The numerical results of inclusive examples confirm the proposed schemes’ theoretical results and illustrate their applicability and efficiency. 2025-03-03T09:11:09Z 2025-03-03T09:11:09Z 2025 Статья Alikhanov A.A., Yadav P., Singh V.K., Asl M.S. A high-order compact difference scheme for the multi-term time-fractional Sobolev-type convection-diffusion equation // Computational and Applied Mathematics. - 2024. - 44 (1). - art. no. 115. - DOI: 10.1007/s40314-024-03077-8 https://dspace.ncfu.ru/handle/123456789/29834 en Journal of Computational and Applied Mathematics application/pdf application/pdf Springer Nature |
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| topic |
Caputo time-fractional derivative Stability and Convergence Multi-term Sobolev type equation L2 formula Compact difference scheme |
| spellingShingle |
Caputo time-fractional derivative Stability and Convergence Multi-term Sobolev type equation L2 formula Compact difference scheme Alikhanov, A. A. Алиханов, А. А. Shahbazi Asl, M. Шахбазиасль, М. A high-order compact difference scheme for the multi-term time-fractional Sobolev-type convection-diffusion equation |
| description |
This paper presents two high-order compact difference schemes to discuss the numerical solution of the one-dimensional and two-dimensional multi-term time-fractional convection-diffusion equation of the Sobolev type based on the Caputo fractional derivative. For this purpose, we employ the L2 formula for the temporal discretization of the Caputo fractional derivatives and introduce a new compact difference operator for the space discretization. The proposed schemes transform the original problem into a system of algebraic equation. We present a novel analysis of the convergence and theoretical stability of both methods. The difference schemes have fourth-order and 3-max{αr,βr} order of accuracy in space and time respectively, where αr and βr are the orders of the fractional derivatives in the multi-term convection-diffusion model. Additionally, we construct an L2-type numerical scheme on non-uniform graded meshes to address problems where the solution exhibits weak initial regularity. Some test functions are provided to demonstrate the accuracy and efficiency of the proposed schemes. The numerical results of inclusive examples confirm the proposed schemes’ theoretical results and illustrate their applicability and efficiency. |
| format |
Статья |
| author |
Alikhanov, A. A. Алиханов, А. А. Shahbazi Asl, M. Шахбазиасль, М. |
| author_facet |
Alikhanov, A. A. Алиханов, А. А. Shahbazi Asl, M. Шахбазиасль, М. |
| author_sort |
Alikhanov, A. A. |
| title |
A high-order compact difference scheme for the multi-term time-fractional Sobolev-type convection-diffusion equation |
| title_short |
A high-order compact difference scheme for the multi-term time-fractional Sobolev-type convection-diffusion equation |
| title_full |
A high-order compact difference scheme for the multi-term time-fractional Sobolev-type convection-diffusion equation |
| title_fullStr |
A high-order compact difference scheme for the multi-term time-fractional Sobolev-type convection-diffusion equation |
| title_full_unstemmed |
A high-order compact difference scheme for the multi-term time-fractional Sobolev-type convection-diffusion equation |
| title_sort |
high-order compact difference scheme for the multi-term time-fractional sobolev-type convection-diffusion equation |
| publisher |
Springer Nature |
| publishDate |
2025 |
| url |
https://dspace.ncfu.ru/handle/123456789/29834 |
| work_keys_str_mv |
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