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Meshless upwind local radial basis function-finite difference technique to simulate the time- fractional distributed-order advection–diffusion equation

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Abstract

The main objective in this paper is to propose an efficient numerical formulation for solving the time-fractional distributed-order advection–diffusion equation. First, the distributed-order term has been approximated by the Gauss quadrature rule. In the next, a finite difference approach is applied to approximate the temporal variable with convergence order \(\mathcal{O}(\tau ^{2-\alpha })\) as \(0<\alpha <1\). Finally, to discrete the spacial dimension, an upwind local radial basis function-finite difference idea has been employed. In the numerical investigation, the effect of the advection coefficient has been studied in terms of accuracy and stability of the proposed difference scheme. At the end, two examples are studied to approve the impact and ability of the numerical procedure.

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Acknowledgements

The authors are very grateful to the reviewers for carefully reading this paper and for their comments and suggestions which have improved the paper.

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  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran

    Mostafa Abbaszadeh & Mehdi Dehghan

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  1. Mostafa Abbaszadeh
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  2. Mehdi Dehghan
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Correspondence to Mostafa Abbaszadeh.

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Abbaszadeh, M., Dehghan, M. Meshless upwind local radial basis function-finite difference technique to simulate the time- fractional distributed-order advection–diffusion equation. Engineering with Computers 37, 873–889 (2021). https://doi.org/10.1007/s00366-019-00861-7

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