Numerical methods for the time-fractional diffusion equation: A review

	Numerical methods for the time-fractional diffusion equation: A review
AUT Journal of Mathematics and Computing
دوره 7، شماره 2، 2026، صفحه 213-269 اصل مقاله (2.24 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 Grünwald-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
مراجع

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