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A numerical solution of time-fractional mixed diffusion and diffusion-wave equation by an RBF-based meshless method

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Abstract

In this paper, we have developed an radial basis function (RBF) based meshless method to solve the time-fractional mixed diffusion and diffusion-wave equation which involves two fractional Caputo derivatives of order \(\alpha \in (0,1)\) and \(\beta \in (1,2)\). The unconditional stability of the proposed numerical scheme is discussed and proved theoretically. The time semi discretization has been done by using the finite difference method and for space discretization, we proposed an RBF-based local collocation method. Some test problems are considered for regular as well as an irregular domain with uniform and non-uniform points to validate the efficiency and accuracy of the method.

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Acknowledgements

The authors thank the anonymous referees for their valuable comments and suggestions, which helped us to improve the presentation of the work.

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  1. Department of Basic Sciences and Humanities, Rajiv Gandhi Institute of Petroleum Technology, Jais, Amethi, 229304, India

    Akanksha Bhardwaj & Alpesh Kumar

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  1. Akanksha Bhardwaj
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Correspondence to Alpesh Kumar.

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Bhardwaj, A., Kumar, A. A numerical solution of time-fractional mixed diffusion and diffusion-wave equation by an RBF-based meshless method. Engineering with Computers 38, 1883–1903 (2022). https://doi.org/10.1007/s00366-020-01134-4

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