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A Novel Error Analysis of Spectral Method for the Anomalous Subdiffusion Problems with Multi-term Time-fractional Derivative

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Abstract

This paper aims to extend a space-time spectral method to address the multi-term time-fractional subdiffusion equations with Caputo derivative. In this method, the Jacobi polynomials are adopted as the basis functions for temporal discretization and the Lagrangian polynomials are used for spatial discretization. An efficient spectral approximation of the weak solution is established. The main work is the demonstration of the well-posedness for the weak problem and the derivation of a posteriori error estimates for the spectral Galerkin approximation. Extensive numerical experiments are presented to perform the validity of a posteriori error estimators, which support our theoretical results.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 520631, China

    Bo Tang, Yan-ping Chen, Bin Xie & Xiu-xiu Lin

Authors
  1. Bo Tang
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  2. Yan-ping Chen
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  3. Bin Xie
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  4. Xiu-xiu Lin
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Correspondence to Yan-ping Chen.

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Additional information

This work is supported by the State Key Program of National Natural Science Foundation of China (Nos. 11931003) and National Natural Science Foundation of China (Nos. 41974133).

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Tang, B., Chen, Yp., Xie, B. et al. A Novel Error Analysis of Spectral Method for the Anomalous Subdiffusion Problems with Multi-term Time-fractional Derivative. Acta Math. Appl. Sin. Engl. Ser. 39, 943–961 (2023). https://doi.org/10.1007/s10255-023-1091-2

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  • DOI: https://doi.org/10.1007/s10255-023-1091-2

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