On stability and convergence of L2-1_σ method on general nonuniform meshes for subdiffusion equation

08/02/2022

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by   Chaoyu Quan, et al.

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In this work the L2-1_σ method on general nonuniform meshes is studied for the subdiffusion equation. Under some constraints on the time step ratio ρ_k, for example ρ_k≥ 0.475329 for all k≥ 2, a crucial bilinear form associated with the L2-1_σ fractional-derivative operator is proved to be positive semidefinite and the H^1-stability of L2-1_σ schemes is then derived for all time under simple assumptions on the initial condition and the source term. In addition, we prove the sharp convergence when ρ_k≥ 0.475329, which reduces the restriction ρ_k≥ 4/7 proposed by Liao, McLean and Zhang in [SIAM J. Numer. Anal. 57 (2019), no. 1, 218-237].