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An implicit nonlinear difference scheme for two-dimensional time-fractional Burgers’ equation with time delay

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Abstract

In this paper, based on the L1 discretization for the Caputo fractional derivative, a fully implicit nonlinear difference scheme with (\(2-\alpha \))-th order accuracy in time and second-order accuracy in space is proposed to solve the two-dimensional time-fractional Burgers’ equation with time delay, where \(\alpha \in \) (0,1) is the fractional order. The existence of the numerical scheme is studied by the Browder fixed point theorem. Furthermore, with the help of a fractional Grönwall inequality, the constructed scheme is verified to be unconditionally stable and convergent in \(L_2\) norm by using the energy method. Finally, a numerical example is given to illustrate the correctness of our theoretical analysis.

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Acknowledgements

The authors would like to thank the editor and reviewers for their constructive comments and suggestions, which helped the authors to improve the quality of the paper significantly.

Funding

This research is supported by the National Natural Science Foundation of China (No. 11701103), Young Top-notch Talent Program of Guangdong Province (No. 2017GC010379), Natural Science Foundation of Guangdong Province (No. 2022A1515012147, 2023A1515011504), the Project of Science and Technology of Guangzhou (No. 202102020704), the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University (2021023).

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  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, 510006, Guangdong, China

    Mingcong Xiao, Zhibo Wang & Yan Mo

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  1. Mingcong Xiao
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  2. Zhibo Wang
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  3. Yan Mo
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Correspondence to Zhibo Wang.

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Xiao, M., Wang, Z. & Mo, Y. An implicit nonlinear difference scheme for two-dimensional time-fractional Burgers’ equation with time delay. J. Appl. Math. Comput. 69, 2919–2934 (2023). https://doi.org/10.1007/s12190-023-01863-x

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  • DOI: https://doi.org/10.1007/s12190-023-01863-x

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