Abstract
This paper studies a new computational method for the approximate solution of the space fractional advection–dispersion equation in sense of Caputo derivatives. In the first method, a time discretization is accomplished via the compact finite difference, while the fourth kind shifted Chebyshev polynomials are used to discretize the spatial derivative. The unconditional stability and convergence order of the method are studied via the energy method. Three examples are given for illustrating the effectiveness and accuracy of the new scheme when compared with existing numerical methods reported in the literature.
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Acknowledgements
The authors are thankful to the respected reviewers for their valuable comments and constructive suggestions towards the improvement of the original paper. The authors are also very grateful to the Associate Editor, Professor Vasily E. Tarasov for managing the review process.
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Mesgarani, H., Rashidinia, J., Aghdam, Y.E. et al. Numerical treatment of the space fractional advection–dispersion model arising in groundwater hydrology. Comp. Appl. Math. 40, 22 (2021). https://doi.org/10.1007/s40314-020-01410-5
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DOI: https://doi.org/10.1007/s40314-020-01410-5
Keywords
- Space fractional advection–dispersion equation
- Compact finite difference
- Chebyshev collocation method
- Error analysis