An efficient approximate solution of Riesz fractional advection-diffusion equation

Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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JR_CMDE-10-2_002

تاریخ نمایه سازی: 9 بهمن 1401

Abstract:

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 [−۱, ۱] × [−۱, ۱]. 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.

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Authors

Siavash Mockary

Department of Mathematics, College of Science, Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran.

Alireza Vahidi

Department of Mathematics, College of Science, Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran.

Esmail Babolian

Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.

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