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Local discontinuous Galerkin method for a hidden-memory variable order reaction–diffusion equation

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Abstract

A high-order numerical method for a hidden-memory variable order reaction–diffusion equation is investigated in this paper. We propose the local discontinuous Galerkin method and a finite difference scheme to discrete the spatial and temporal variables, respectively. This paper provides an effective decomposition strategy for dealing with the monotonic loss of temporal discretization coefficients caused by changing order. The scheme is proved to be unconditionally stable and convergent with \({\textrm{O}}(\tau +{h^{k+1}})\), where \(\tau \) is the temporal step, h is the spatial step and k is the degree of the piecewise \(P^k\) polynomial. Some numerical examples are carried out to show the effectiveness of the scheme and confirm the theoretical convergence rates.

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Acknowledgements

We would like to thank Dr. Xindong Zhang for his valuable discussions that helped us improve the manuscript.

Funding

This work is supported by the State Key Program of National Natural Science Foundation of China (11931003) and National Natural Science Foundation of China (41974133), the Training Plan of Young Backbone Teachers in Henan University of Technology of China (21420049), and Scientific and Technological Research Projects in Henan Province (212102210612).

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Authors and Affiliations

  1. College of Science, Henan University of Technology, Zhengzhou, 450001, Henan, People’s Republic of China

    Leilei Wei & Huanhuan Wang

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, Guangdong, People’s Republic of China

    Yanping Chen

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  1. Leilei Wei
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  2. Huanhuan Wang
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  3. Yanping Chen
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All authors contributed equally to the manuscript and read and approved the final manuscript.

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Correspondence to Yanping Chen.

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Wei, L., Wang, H. & Chen, Y. Local discontinuous Galerkin method for a hidden-memory variable order reaction–diffusion equation. J. Appl. Math. Comput. 69, 2857–2872 (2023). https://doi.org/10.1007/s12190-023-01865-9

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  • DOI: https://doi.org/10.1007/s12190-023-01865-9

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