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Engineering with Computers

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

  • 18-07-2020
  • Original Article
Published in:
Authors
H. Safdari
Y. Esmaeelzade Aghdam
J. F. Gómez-Aguilar
Published in
Engineering with Computers | Issue 2/2022

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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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Title
Shifted Chebyshev collocation of the fourth kind with convergence analysis for the space–time fractional advection-diffusion equation
Authors
H. Safdari
Y. Esmaeelzade Aghdam
J. F. Gómez-Aguilar
Publication date
18-07-2020
Publisher
Springer London
Published in
Engineering with Computers / Issue 2/2022
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-020-01092-x
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