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


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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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 (2020). https://doi.org/10.1007/s40096-020-00346-5

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  • 3D time-fractional diffusion equation
  • Compact scheme
  • Finite difference method
  • Alternating direction implicit method
  • Caputo–Fabrizio operator