发表机构
School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen; Department of Applied Mathematics, The Hong Kong Polytechnic University（香港中文大学深圳校区科学与工程学院; 香港理工大学应用数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出统一框架，建立L²梯度流的保平衡ETDRK方法的原始能量耗散，推导时间步长限制，数值实验证实理论结果。
AI 中文摘要
本文开发了一个统一框架，用于建立L²梯度流的保平衡指数时间差分Runge-Kutta（ETDRK）方法的原始能量耗散。该分析基于一般ETDRK方法的辅助连续演化表示，这使得能量变化可被控制，无需对Butcher系数施加正定条件或引入稳定项。针对一大类保平衡ETDRK格式，我们推导了显式可计算的时间步长限制；对2阶至5阶的代表性格式获得了显式限制，且该框架也适用于任意高阶的基于插值的ETDRK方法。对于后一类方法，所得的可容许步长显著大于先前基于插值的特定分析得到的步长。对Allen-Cahn方程的数值实验证实了理论耗散限制。
英文摘要
This paper develops a unified framework for establishing original energy dissipation of equilibrium-preserving exponential time differencing Runge--Kutta (ETDRK) methods for $L^2$ gradient flows. The analysis is based on an auxiliary continuous evolution representation of a general ETDRK method, which allows the energy variation to be controlled without imposing positive-definiteness conditions on the Butcher coefficients or introducing stabilization terms. For a broad class of equilibrium-preserving ETDRK schemes, we derive an explicitly computable time-step restriction. Explicit restrictions are obtained for representative schemes of orders two through five, and the framework also applies to arbitrarily high-order interpolation-based ETDRK methods. For the latter class, the resulting admissible step sizes are substantially larger than those obtained from the previous interpolation-specific analysis. Numerical experiments for the Allen--Cahn equation confirm the theoretical dissipation restrictions.
