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math.NA2023★ 2 cited
A novel high-order linearly implicit and energy-stable additive Runge-Kutta methods for gradient flow models
Xuelong Gu, Wenjun Cai, Yushun Wang
This paper introduces a novel paradigm for constructing linearly implicit and high-order unconditionally energy-stable schemes for general gradient flows, utilizing the scalar auxi…
math.NA2023
Energy stable and maximum bound principle preserving schemes for the Allen-Cahn equation based on the Saul'yev methods
Xuelong Gu, Yushun Wang, Wenjun Cai
The energy dissipation law and maximum bound principle are significant characteristics of the Allen-Chan equation. To preserve discrete counterpart of these properties, the linear…