Chebyshev spectral method for the variable-order fractional mobile–immobile advection–dispersion equation arising from solute transport in heterogeneous media

This study focuses on the numerical solution of the space–time variable-order fractional derivative mobile–immobile advection–dispersion equation. These equations are preferred for dynamical system modeling, which includes determining the solute transport mechanism. We take into account the Caputo c...

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Bibliographic Details
Published inJournal of engineering mathematics Vol. 142; no. 1
Main Authors Gupta, Rupali, Kumar, Sushil
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.10.2023
Springer Nature B.V
Subjects
Advection
Applications of Mathematics
Chebyshev approximation
Collocation methods
Computational Mathematics and Numerical Analysis
Convergence
Dispersion
Mathematical analysis
Mathematical and Computational Engineering
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Sobolev space
Spectral methods
Theoretical and Applied Mechanics
Caputo’s variable-order fractional derivative
Mobile–immobile advection–dispersion equation
Collocation method
Chebyshev polynomial
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Summary:This study focuses on the numerical solution of the space–time variable-order fractional derivative mobile–immobile advection–dispersion equation. These equations are preferred for dynamical system modeling, which includes determining the solute transport mechanism. We take into account the Caputo class of fractional derivatives. A Chebyshev collocation method in both the space and time directions is utilized for the approximate solution of the equation. The convergence analysis of the method is shown by using the Chebyshev-weighted Sobolev space. Finally, some examples are provided to illustrate the accuracy and efficiency of the present approach. Comparisons between the results obtained by our method and those obtained by the existing methods are presented to demonstrate the superiority of the proposed methodology. The spectral or exponential convergence of the suggested approach is one of its essential characteristics, which is verified through numerical results and provides additional support for the effectiveness of the suggested technique.
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ISSN:0022-0833
1573-2703
DOI:10.1007/s10665-023-10288-1