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The characteristic difference DDM for solving the time-fractional order convection–diffusion equations

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Abstract

In this paper, an efficient characteristic difference domain decomposition method for solving the time-fractional order convection–diffusion equations is developed. A three-step method is used to solve the solution over non-overlapping sub-domain at every time interval. The new solutions are first solved by the the quadratic interpolation. Then, the intermediate fluxes on the interfaces of sub-domains are computed by local multi-point weighted average from the above new solutions. Finally, the solutions and fluxes in the interiors of sub-domains are computed by the implicit characteristic difference method, while the time fractional derivative is approximated by L1-format. By combining the operator splitting technique, we further propose an efficient splitting domain decomposition method for solve the two-dimensional problems. By some auxiliary lemmas, the stability and error estimate are given in discrete \(L^2\)-norm. We further prove that our scheme is of second-order convergence in space and of first-order convergence in time. Numerical experiments are presented to validate theoretical result.

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Acknowledgements

This work was supported by Natural Science Foundation of China (Grant No. 61703250), Natural Science Foundation of Shandong Government (Grant No. ZR2021MA002), and Shandong Agricultural University (Grant No. xxxy201704).

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Authors and Affiliations

  1. School of Information Science and Engineering, Shandong Agricultural University, Taian, 271018, Shandong, China

    Zhongguo Zhou, Ning Wang, Hao Pan & Yan Wang

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  1. Zhongguo Zhou
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  2. Ning Wang
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  3. Hao Pan
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  4. Yan Wang
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Correspondence to Zhongguo Zhou.

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Zhou, Z., Wang, N., Pan, H. et al. The characteristic difference DDM for solving the time-fractional order convection–diffusion equations. Comp. Appl. Math. 42, 289 (2023). https://doi.org/10.1007/s40314-023-02429-0

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