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The long time error estimates for the second order backward difference approximation to sub-diffusion equations with boundary time delay and feedback gain

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  • Xu, Da

Abstract

We consider time fractional diffusion initial boundary value problem with boundary time delay and feedback gain involving two Caputo fractional derivatives in time. When both the time delay and feedback gain are taken as appropriately small such that the characteristic equation has no solution in the location of the right half plane of the imaginary axis, we derive the solution’s existence, uniqueness and representation. The second-order backward difference time discrete schemes are investigated in time discretization. The lt∞(0,∞;L2) error analysis of the numerical schemes is derived when both the time delay and feedback gain are appropriately small such that the characteristic equation of the discrete problem has no solution in a strip of the right half plane of the imaginary axis, and the order of boundary Caputo fractional derivative is equal to the order or half order of interior domain Caputo fractional derivative. The numerical examples illustrate its accuracy, efficiency and robustness, and are consistent with the theoretical results.

Suggested Citation

  • Xu, Da, 2023. "The long time error estimates for the second order backward difference approximation to sub-diffusion equations with boundary time delay and feedback gain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 186-206.
    • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:186-206
    DOI: 10.1016/j.matcom.2023.01.027
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    References listed on IDEAS

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    1. Liu, Jun & Fu, Hongfei & Zhang, Jiansong, 2020. "A QSC method for fractional subdiffusion equations with fractional boundary conditions and its application in parameters identification," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 153-174.
    2. Hendy, Ahmed S. & Zaky, Mahmoud A. & Abbaszadeh, Mostafa, 2021. "Long time behavior of Robin boundary sub-diffusion equation with fractional partial derivatives of Caputo type in differential and difference settings," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1370-1378.
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