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A second-order difference scheme for two-dimensional two-sided space distributed-order fractional diffusion equations with variable coefficients

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Abstract

In this paper, a second-order difference scheme is developed to solve two-dimensional two-sided space distributed-order fractional diffusion equation with variable coefficients. In the spatial direction, a second-order difference scheme is proposed, the distribution-order integral is discretized by the Gauss–Legendre quadrature formula and the space fractional derivative is approximated by the weighted and shifted Grünwald–Letnikov operators. In addition, the time direction is discretized into a second-order difference scheme by the Crank–Nicolson method. Therefore, the main numerical scheme is developed. Furthermore, a small perturbation is added to the main difference scheme to construct an alternating-direction implicit scheme. Also, the stability and convergence of the numerical scheme are proved. Finally, some numerical results are provided to show the accuracy and efficiency of the proposed method.

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Acknowledgements

The authors thank the reviewers for their comments, which have significantly improved the presentation.

Funding

The authors would like to acknowledge the support provided by the National Natural Science Foundation of China (12101089) and the Natural Science Foundation of Sichuan Province (2022NSFSC1844).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

    Yifei Wang & Jin Huang

  2. School of Mathematics, Chengdu Normal University, Chengdu, 611130, China

    Hu Li

Authors
  1. Yifei Wang
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  2. Jin Huang
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  3. Hu Li
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All authors wrote the main manuscript text include Sects. 1–5. All authors reviewed the manuscript.

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Correspondence to Jin Huang.

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Wang, Y., Huang, J. & Li, H. A second-order difference scheme for two-dimensional two-sided space distributed-order fractional diffusion equations with variable coefficients. J. Appl. Math. Comput. 70, 1–26 (2024). https://doi.org/10.1007/s12190-023-01954-9

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