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A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation

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Abstract

This paper deals with the design and analysis of a high-order numerical scheme for the two-dimensional time-fractional reaction-subdiffusion equation. The time-fractional derivative of order α, (α ∈ (0,1)) in the model problem is approximated by means of the L2 − 1σ scheme and the space derivatives are discretized by means of a compact alternating direction implicit (ADI) finite difference scheme. Convergence and stability of the method are analyzed. Five numerical examples are provided to demonstrate the applicability and accuracy of the method. It is shown that the method is unconditionally stable and is of \(\mathcal {O}({\Delta } t^{1+\alpha }+{h_{x}^{4}}+{h_{y}^{4}})\) accuracy, where Δt is the temporal step size and hx and hy are the spatial step sizes. The computed results are in good agreement with the theoretical analysis. Moreover, the comparison with the corresponding results of existing methods demonstrates that our method has advantages in convergence order and error improvement when solving the time-fractional reaction-subdiffusion equation. The CPU time consumed by the proposed method is provided.

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Acknowledgements

The authors would like to thank the editor and anonymous referees for their valuable suggestions and comments which helped us to improve the quality of the manuscript.

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  1. Department of Mathematics, VNIT, Nagpur, 440010, India

    Pradip Roul & Vikas Rohil

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  1. Pradip Roul
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  2. Vikas Rohil
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Correspondence to Pradip Roul.

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Roul, P., Rohil, V. A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation. Numer Algor 90, 1357–1387 (2022). https://doi.org/10.1007/s11075-021-01233-3

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  • DOI: https://doi.org/10.1007/s11075-021-01233-3

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