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Numerical investigation of a difference scheme for the multi-term time-space Caputo-Riesz fractional diffusion equations | ||
| Journal of New Researches in Mathematics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 بهمن 1401 | ||
| نوع مقاله: research paper | ||
| شناسه دیجیتال (DOI): 10.30495/jnrm.2023.63765.2165 | ||
| نویسندگان | ||
Mojtaba Fardi1؛ Ebrahim Amini  2
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| 1Faculaty of Mathematical sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran (E-mail: mojtaba.fardi@gmail.com) | ||
| 2Department of Mathematics, Payme Noor University, P. O. Box 19395-4697, Tehran, IRAN | ||
| چکیده | ||
| .Abstract: In this paper, we provide a difference scheme for solving multi-term the time-space fractional diffusion equations. In fractional diffusion equations, the time derivative is of the Caputo type and the space derivative is of the Riesz type. The aformentional equations are considered for one and two dimensional. In one dimentional the Riesz space derivative is of the order and in two dimentional the Riesz space derivative is of the orders and . Also, the multi-term Caputo derivative is of orders . We provided the stability and convergence analysis of the proposed difference scheme and investigate the stability conditions of the proposed difference scheme. We prove that the proposed difference scheme is stable conditionally. Furthermore, we show that difference scheme is convergent with order in time and order 2 in space. Finally, we give two numerical examples for one and two dimensional to illustrate the efficiency and applicability of the proposed difference scheme in the sense of accuracy and convergence ratio. | ||
| کلیدواژهها | ||
| Fractional diffusion equations؛ Caputo-Riesz derivative؛ Difference scheme؛ stable Conditionally؛ Convergence | ||
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آمار تعداد مشاهده مقاله: 89 |
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