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Shifted Chebyshev collocation of the fourth kind with convergence analysis for the space–time fractional advection-diffusion equation

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Abstract

The main purpose of this paper is to design a numerical method for solving the space–time fractional advection-diffusion equation (STFADE). First, a finite difference scheme is applied to obtain the semi-discrete in time variable with convergence order \(\mathcal {O}(\tau ^{2-\beta })\). In the next, to discrete the spatial fractional derivative, the Chebyshev collocation method of the fourth kind has been applied. This discrete scheme is based on the closed formula for the spatial fractional derivative. Besides, the time-discrete scheme has studied in the \(L_{2}\) space by the energy method and we have proved the unconditional stability and convergence order. Finally, we solve three examples by the proposed method and the obtained results are compared with other numerical problems. The numerical results show that our method is much more accurate than existing techniques in the literature.

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Acknowledgements

José Francisco Gómez Aguilar affirms the help provided by CONACyT, Mexico: Cátedras CONACyT para jóvenes investigators 2014 and SNI-CONACyT, Mexico.

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Authors and Affiliations

  1. Faculty of Science, Shahid Rajaee Teacher Training University, Lavizan, Tehran, 16785-163, Iran

    H. Safdari & Y. Esmaeelzade Aghdam

  2. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico

    J. F. Gómez-Aguilar

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  1. H. Safdari
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  2. Y. Esmaeelzade Aghdam
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  3. J. F. Gómez-Aguilar
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Correspondence to J. F. Gómez-Aguilar.

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Safdari, H., Aghdam, Y.E. & Gómez-Aguilar, J.F. Shifted Chebyshev collocation of the fourth kind with convergence analysis for the space–time fractional advection-diffusion equation. Engineering with Computers 38, 1409–1420 (2022). https://doi.org/10.1007/s00366-020-01092-x

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