An efficient approximate solution of Riesz fractional advection-diffusion equation

Document Type : Research Paper

Authors

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

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

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 [−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.

Keywords

References

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Computational Methods for Differential Equations
Volume 10, Issue 2
April 2022
Pages 307-319

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History

  • Receive Date: 25 September 2020
  • Revise Date: 04 April 2021
  • Accept Date: 11 April 2021

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