In this paper, a pseudo-spectral method with the Lagrange polynomial basis is proposed to solve the time-fractional advection-diffusion equation. A semi-discrete approximation scheme is used for conversion of this equation to a system of ordinary fractional differential equations. Also, to protect the high accuracy of the spectral approximation, the Mittag-Leffler function is used for the integration along the time variable. Some examples are performed to illustrate the accuracy and efficiency of the proposed method.
Shokri, A. and Mirzaei, S. (2020). A pseudo-spectral based method for time-fractional advection-diffusion equation. Computational Methods for Differential Equations, 8(3), 454-467. doi: 10.22034/cmde.2020.29307.1414
MLA
Shokri, A. , and Mirzaei, S. . "A pseudo-spectral based method for time-fractional advection-diffusion equation", Computational Methods for Differential Equations, 8, 3, 2020, 454-467. doi: 10.22034/cmde.2020.29307.1414
HARVARD
Shokri, A., Mirzaei, S. (2020). 'A pseudo-spectral based method for time-fractional advection-diffusion equation', Computational Methods for Differential Equations, 8(3), pp. 454-467. doi: 10.22034/cmde.2020.29307.1414
CHICAGO
A. Shokri and S. Mirzaei, "A pseudo-spectral based method for time-fractional advection-diffusion equation," Computational Methods for Differential Equations, 8 3 (2020): 454-467, doi: 10.22034/cmde.2020.29307.1414
VANCOUVER
Shokri, A., Mirzaei, S. A pseudo-spectral based method for time-fractional advection-diffusion equation. Computational Methods for Differential Equations, 2020; 8(3): 454-467. doi: 10.22034/cmde.2020.29307.1414
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