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., 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
Ali Shokri; Soheila 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
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
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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