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The meshless approach for solving 2D variable-order time-fractional advection–diffusion equation arising in anomalous transport

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Abstract

In this paper, with the aim of extending an elegant and straightforward numerical approximation to describe one of the most common physical phenomena has been undertaken. In this regard, the generalization of advection–diffusion equation, namely, the time-fractional advection–diffusion equation with understanding sense variable-order fractional derivative, is taken into consideration. An efficient and accurate approach is relying on the Kansa scheme and finite difference method to provide a mathematical framework to treat the spatial discretization and temporal term, respectively. The meshless collocation approach is utilized for interior scattered points and those on the boundary. Thus, the problem under consideration is reduced to a system of linear algebraic equations. The use of the radial basis function as shape function brings many advantages for proposal numerical method in terms of improved accuracy by setting an appropriate shape parameter and applied for solving high-dimensional models without extra cost. The validity and accuracy of the proposed approach is investigated by four various examples involving three benchmark examples and a practical application of pollution transfer phenomena.

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Acknowledgements

“This work is supported by the National Science Foundation of China (NSFC), Grant No. 11962017”.

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Authors and Affiliations

  1. Institute for Advanced Study, Nanchang University, Nanchang, 330031, China

    Vahid Reza Hosseini & W.-N. Zou

  2. Department of Civil Engineering, University of Qom, Qom, Iran

    Masoumeh Koushki

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  1. Vahid Reza Hosseini
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  3. W.-N. Zou
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Correspondence to W.-N. Zou.

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Hosseini, V.R., Koushki, M. & Zou, WN. The meshless approach for solving 2D variable-order time-fractional advection–diffusion equation arising in anomalous transport. Engineering with Computers 38 (Suppl 3), 2289–2307 (2022). https://doi.org/10.1007/s00366-021-01379-7

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