35 citations · 86 across the 4 of their papers we have counts for
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math.NA2023★ 25 cited
Asymptotically compatible energy and dissipation law of the nonuniform L2- scheme for time fractional Allen-Cahn model
Hong-lin Liao, Xiaohan Zhu, Hong Sun
We build an asymptotically compatible energy of the variable-step L2- scheme for the time-fractional Allen-Cahn model with the Caputo's fractional derivative of order $α\in(0,…
math.NA2022★ 23 cited
Energy stability of variable-step L1-type schemes for time-fractional Cahn-Hilliard model
Bingquan Ji, Xiaohan Zhu, Hong-lin Liao
The positive definiteness of discrete time-fractional derivatives is fundamental to the numerical stability (in the energy sense) for time-fractional phase-field models. A novel te…
math.NA2021★ 35 cited
The variable-step L1 scheme preserving a compatible energy law for time-fractional Allen-Cahn equation
Hong-lin Liao, Xiaohan Zhu, Jindi Wang
In this work, we revisit the adaptive L1 time-stepping scheme for solving the time-fractional Allen-Cahn equation in the Caputo's form. The L1 implicit scheme is shown to preserve…