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Mockary, Siavash, Vahidi, Alireza, Babolian, Esmail. (1401). An efficient approximate solution of Riesz fractional advection-diffusion equation. سامانه مدیریت نشریات علمی, 10(2), 307-319. doi: 10.22034/cmde.2021.41690.1815
Siavash Mockary; Alireza Vahidi; Esmail Babolian. "An efficient approximate solution of Riesz fractional advection-diffusion equation". سامانه مدیریت نشریات علمی, 10, 2, 1401, 307-319. doi: 10.22034/cmde.2021.41690.1815
Mockary, Siavash, Vahidi, Alireza, Babolian, Esmail. (1401). 'An efficient approximate solution of Riesz fractional advection-diffusion equation', سامانه مدیریت نشریات علمی, 10(2), pp. 307-319. doi: 10.22034/cmde.2021.41690.1815
Mockary, Siavash, Vahidi, Alireza, Babolian, Esmail. An efficient approximate solution of Riesz fractional advection-diffusion equation. سامانه مدیریت نشریات علمی, 1401; 10(2): 307-319. doi: 10.22034/cmde.2021.41690.1815

An efficient approximate solution of Riesz fractional advection-diffusion equation

Computational Methods for Differential Equations
مقاله 2، دوره 10، شماره 2، تیر 2022، صفحه 307-319    اصل مقاله (389.42 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.41690.1815
نویسندگان
Siavash Mockary1؛ Alireza Vahidi* 1؛ Esmail Babolian2
1Department of Mathematics, College of Science, Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran.
2Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.
چکیده
The Riesz fractional advection-diffusion is a result of the mechanics of chaotic dynamics. It’s of preponderant importance to solve this equation numerically. Moreover, the utilization of Chebyshev polynomials as a base in several mathematical equations shows the exponential rate of convergence. To this approach, we transform the interval of state space into the interval [−1, 1] × [−1, 1]. Then, we use the operational matrix to discretize fractional operators. Applying the resulting discretization, we obtain a linear system of equations, which leads to the numerical solution. Examples show the effectiveness of the method.
کلیدواژه‌ها
Operational matrices؛ Chebyshev polynomials؛ Fractional partial differential equations؛ Riesz fractional advection-diffusion
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