TY - JOUR
ID - 12721
TI - An efficient approximate solution of Riesz fractional advection-diffusion equation
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Mockary, Siavash
AU - Vahidi, Alireza
AU - Babolian, Esmail
AD - Department of Mathematics, College of Science, Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran.
AD - Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.
Y1 - 2022
PY - 2022
VL - 10
IS - 2
SP - 307
EP - 319
KW - Operational matrices
KW - Chebyshev polynomials
KW - fractional partial differential equations
KW - Riesz fractional advection-diffusion
DO - 10.22034/cmde.2021.41690.1815
N2 - 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.
UR - https://cmde.tabrizu.ac.ir/article_12721.html
L1 - https://cmde.tabrizu.ac.ir/article_12721_1cb3cc01abce405e339fc8c370263ba6.pdf
ER -