%0 Journal Article
%T An efficient approximate solution of Riesz fractional advection-diffusion equation
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Mockary, Siavash
%A Vahidi, Alireza
%A Babolian, Esmail
%D 2022
%\ 04/01/2022
%V 10
%N 2
%P 307-319
%! An efficient approximate solution of Riesz fractional advection-diffusion equation
%K Operational matrices
%K Chebyshev polynomials
%K fractional partial differential equations
%K Riesz fractional advection-diffusion
%R 10.22034/cmde.2021.41690.1815
%X 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.
%U https://cmde.tabrizu.ac.ir/article_12721_1cb3cc01abce405e339fc8c370263ba6.pdf