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A high-order compact alternating direction implicit method for solving the 3D time-fractional diffusion equation with the Caputo–Fabrizio operator

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Abstract

In this paper, a high-order compact finite difference method (CFDM) with an operator-splitting technique for solving the 3D time-fractional diffusion equation is considered. The Caputo–Fabrizio time operator is evaluated by the \(L_1\) approximation, and the second-order space derivatives are approximated by the compact CFDM to obtain a discrete scheme. Alternating direction implicit method (ADI) is used to split the problem into three separate one-dimensional problems. The local truncation error analysis is discussed. Moreover, the convergence and stability of the numerical method are investigated. Finally, some numerical examples are presented to demonstrate the accuracy of the compact ADI method.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

    Narjes Abdi, Hossein Aminikhah & Javad Alavi

  2. Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, Rasht, Iran

    Hossein Aminikhah

  3. Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran

    Amir Hossein Refahi Sheikhani

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  1. Narjes Abdi
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  2. Hossein Aminikhah
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  3. Amir Hossein Refahi Sheikhani
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  4. Javad Alavi
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Correspondence to Hossein Aminikhah.

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Abdi, N., Aminikhah, H., Refahi Sheikhani, A. et al. A high-order compact alternating direction implicit method for solving the 3D time-fractional diffusion equation with the Caputo–Fabrizio operator. Math Sci 14, 359–373 (2020). https://doi.org/10.1007/s40096-020-00346-5

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  • DOI: https://doi.org/10.1007/s40096-020-00346-5

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