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Numerical methods for the time-fractional diffusion equation: A review | ||
| AUT Journal of Mathematics and Computing | ||
| دوره 7، شماره 2، تیر 2026، صفحه 213-269 اصل مقاله (2.58 M) | ||
| نوع مقاله: Review Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2026.24592.1441 | ||
| نویسندگان | ||
| Amin Ghoreyshi؛ Mostafa Abbaszadeh* ؛ Mehdi Dehghan | ||
| Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, Iran | ||
| چکیده | ||
| This review paper focuses on the numerical solution of the time-fractional diffusion equation using various discretization techniques. For the time-fractional derivative, we consider methods such as L-type approximations and Grunwald-Letnikov-based formulas, while for the spatial diffusion term, we utilize the compact finite difference method, finite element method, spectral element method, meshless method, Chebyshev spectral method, and finite block method. In addition, stability and convergence theorems are presented, accompanied by numerical examples that confirm the theoretical results. | ||
| کلیدواژهها | ||
| Time-fractional diffusion equation؛ L-type approximations؛ Weighted and shifted Grunwald-Letnikov formulas؛ Finite difference methods؛ Finite element method؛ Meshless method؛ Spectral element method؛ Chebyshev spectral method؛ Finite block method؛ Theoretical analysis | ||
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آمار تعداد مشاهده مقاله: 260 تعداد دریافت فایل اصل مقاله: 69 |
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