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Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation

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Abstract

The sharp pointwise-in-time error estimate of the Grünwald-Letnikov scheme for the initial-boundary value problem of a multi-term time fractional diffusion equation is considered, where the solutions exhibit typical weak singularity at initial time. The Grünwald-Letnikov scheme on uniform mesh is used to discretize the multi-term time fractional Caputo derivative and finite difference method is adopted for spatial discretization. A bound for the stability multipliers is deduced using complete monotonicity, by which stability and α-robust error estimate of the fully discrete scheme are rigorously established. Numerical examples are presented to show the sharpness of the error estimate.

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Funding

The research is supported in part by the National Natural Science Foundation of China under Grant 11801026, and Fundamental Research Funds for the Central Universities (No. 202264006).

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Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, China

    Dewei Cao & Hu Chen

Authors
  1. Dewei Cao
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  2. Hu Chen
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Correspondence to Hu Chen.

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Communicated by: Martin Stynes

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Cao, D., Chen, H. Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation. Adv Comput Math 48, 82 (2022). https://doi.org/10.1007/s10444-022-09999-3

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  • DOI: https://doi.org/10.1007/s10444-022-09999-3

Keywords

Mathematics Subject Classification (2010)