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L1 scheme for solving an inverse problem subject to a fractional diffusion equation
Li, Binjie Xie, Xiaoping Yan, Yubin
Li, Binjie
Xie, Xiaoping
Yan, Yubin
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2023-01-19
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Abstract
This paper considers the temporal discretization of an inverse problem subject to a time fractional diffusion equation. Firstly, the convergence of the L1 scheme is established with an arbitrary sectorial operator of spectral angle ⟨ π ∕ 2, that is the resolvent set of this operator contains {z ∈ ℂ ⧵ {0} ∶ |Arg 𝑧| ⟨ θ} for some π ∕ 2 ⟨ θ ⟨ π. The relationship between the time fractional order α ε (0,1) and the constants in the error estimates is precisely characterized, revealing that the L1 scheme is robust as α approaches 1. Then an inverse problem of a fractional diffusion equation is analyzed, and the convergence analysis of a temporal discretization of this inverse problem is given. Finally, numerical results are provided to confirm the theoretical results.
Citation
Li, B., Xie, X., & Yan, Y. (2023). L1 scheme for solving an inverse problem subject to a fractional diffusion equation. Computers and Mathematics with Applications, 134, 2023, 112-123. https://doi.org/10.1016/j.camwa.2023.01.008
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Elsevier
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Computers and Mathematics with Applications
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0898-1221
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1873-7668