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A numerical method for solving variable-order solute transport models

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Abstract

In this work, a radial basis function (RBF)-based numerical scheme is developed which uses the Coimbra variable time fractional derivative of order \(0<\alpha (t,x)< 1\). The Coimbra derivative can efficiently model a dynamical system whose fractional-order behavior changes with time and space locations. The RBF can effectively approximate spatial derivatives in multi-dimensions. The resulted numerical scheme is RBF–FD type and is validated for solute transport problems in 1D and 2D dimension domains. Various cases of variable-order \(0<\alpha (t,x)< 1\) have been discussed. The present numerical scheme can effectively approximate those variable-order models whose exact solution can not be obtained in a simple way.

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Authors and Affiliations

  1. Department of Basics Sciences, University of Engineering and Technology, Peshawar, Pakistan

    Marjan Uddin & Islam Ud Din

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  1. Marjan Uddin
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  2. Islam Ud Din
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Correspondence to Marjan Uddin.

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Communicated by José Tenreiro Machado.

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Uddin, M., Din, I.U. A numerical method for solving variable-order solute transport models. Comp. Appl. Math. 39, 320 (2020). https://doi.org/10.1007/s40314-020-01355-9

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  • DOI: https://doi.org/10.1007/s40314-020-01355-9

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