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A Single-Step Correction Scheme of Crank–Nicolson Convolution Quadrature for the Subdiffusion Equation

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Abstract

We develop a new correction scheme for time discretization of the subdiffusion equation based on the fractional Crank–Nicolson convolution quadrature. Due to the weak singularity of solution near time \(t=0\), a single-step initial correction of the scheme is proposed with rigorous analysis to render the time discretization of second-order accuracy. Optimal error estimates of the numerical schemes are proved for \(L^2\) initial data based on the integral representations of solutions and resolvent estimates of elliptic operator, with regularity assumptions only on the source term. Numerical examples are presented to demonstrate the performance of the proposed method and the consistency with the theoretical analysis.

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Authors and Affiliations

  1. Beijing Computational Science Research Center, Beijing, 100193, China

    Jilu Wang

  2. School of mathematics and statistics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, China

    Jungang Wang

  3. Beijing Computational Science Research Center, Beijing, 100193, China

    Lihong Yin

Authors
  1. Jilu Wang
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  2. Jungang Wang
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  3. Lihong Yin
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Correspondence to Jungang Wang.

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The research of Jilu Wang and Lihong Yin was partially funded by the National Natural Science Foundation of China (NSFC Grant U1930402). The research of Jungang Wang was supported by the Natural Science Foundation of Shaanxi Province (2020JM-132) and the Fundamental Research Funds for the Central Universities (310201911cx025)

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Wang, J., Wang, J. & Yin, L. A Single-Step Correction Scheme of Crank–Nicolson Convolution Quadrature for the Subdiffusion Equation. J Sci Comput 87, 26 (2021). https://doi.org/10.1007/s10915-021-01419-w

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  • DOI: https://doi.org/10.1007/s10915-021-01419-w

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