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Communications in Analysis and Mechanics

2024, Volume 16, Issue 1: 53-70. doi: 10.3934/cam.2024003
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Research article

Pointwise-in-time $ \alpha $-robust error estimate of the ADI difference scheme for three-dimensional fractional subdiffusion equations with variable coefficients

  • College of Sciences, Hunan University of Technology, Zhuzhou, 412008, China
  • Received: 30 October 2023 Revised: 12 December 2023 Accepted: 02 January 2024 Published: 10 January 2024

  • 65M15, 65M06

  • In this paper, a fully-discrete alternating direction implicit (ADI) difference method is proposed for solving three-dimensional (3D) fractional subdiffusion equations with variable coefficients, whose solution presents a weak singularity at $ t = 0 $. The proposed method is established via the L1 scheme on graded mesh for the Caputo fractional derivative and central difference method for spatial derivative, and an ADI method is structured to change the 3D problem into three 1D problems. Using the modified Grönwall inequality we prove the stability and $ \alpha $-robust convergence. The results presented in numerical experiments are in accordance with the theoretical analysis.

    Citation: Wang Xiao, Xuehua Yang, Ziyi Zhou. Pointwise-in-time $ \alpha $-robust error estimate of the ADI difference scheme for three-dimensional fractional subdiffusion equations with variable coefficients[J]. Communications in Analysis and Mechanics, 2024, 16(1): 53-70. doi: 10.3934/cam.2024003

    Related Papers:

  • In this paper, a fully-discrete alternating direction implicit (ADI) difference method is proposed for solving three-dimensional (3D) fractional subdiffusion equations with variable coefficients, whose solution presents a weak singularity at $ t = 0 $. The proposed method is established via the L1 scheme on graded mesh for the Caputo fractional derivative and central difference method for spatial derivative, and an ADI method is structured to change the 3D problem into three 1D problems. Using the modified Grönwall inequality we prove the stability and $ \alpha $-robust convergence. The results presented in numerical experiments are in accordance with the theoretical analysis.


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