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A novel RBF-based meshless method for solving time-fractional transport equations in 2D and 3D arbitrary domains

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Abstract

In this paper, we develop a new meshless method for solving a wide class of time-fractional partial differential equations with general space operators in 2D and 3D regular and irregular domains. These equations are usually used to model transport processes in anisotropic media with sub-diffusive phenomena. In this method, the spatial approximation is given in the form of the truncated series over a set of linearly independent functions. Then the system is solved by the use of an efficient backward substitution method which is based on the collocation procedure using modified basis functions. The main aim of the research is to show the accuracy and efficiency of the proposed algorithm over some of the existing methods. The numerical results of ten examples on 2D and 3D domains demonstrate the advantages of the presented approach.

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Acknowledgements

We would like to thank the editor and referees for giving valuable improvements to the paper. The work was supported by the National Key Research and Development Program of China (No. 2021YFB2600700), the National Natural Science Foundation of China (Nos. 12072103, 52171272), the Natural Science Foundation of Jiangsu Province (No. BK20190073), the State Key Laboratory of Acoustics, Chinese Academy of Sciences (No. SKLA202001), the Key Laboratory of Intelligent Materials and Structural Mechanics of Hebei Province (No. KF2021-01), and the China Postdoctoral Science Foundation (Nos. 2017M611669, 2018T110430).

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Authors and Affiliations

  1. Key Laboratory of Coastal Disaster and Defence (Ministry of Education), College of Mechanics and Materials, Hohai University, Nanjing, 210098, China

    Ji Lin & Jinge Bai

  2. A. Pidhornyi Institute of Mechanical Engineering Problems of NAS of Ukraine, 2/10 Pozharsky street, 61046, Kharkiv, Ukraine

    Sergiy Reutskiy

  3. Nanjing Hydraulic Research Institute, Nanjing, 210029, China

    Jun Lu

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  1. Ji Lin
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  2. Jinge Bai
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  4. Jun Lu
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Correspondence to Ji Lin or Jun Lu.

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Lin, J., Bai, J., Reutskiy, S. et al. A novel RBF-based meshless method for solving time-fractional transport equations in 2D and 3D arbitrary domains. Engineering with Computers 39, 1905–1922 (2023). https://doi.org/10.1007/s00366-022-01601-0

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