发表机构
University of Trento; University of Verona; University of Padua（特伦托大学; 维罗纳大学; 帕多瓦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文分析非交换算子半线性问题的分裂指数积分器，推导新误差表示并证明分裂指数欧拉与二阶指数龙格-库塔方法的收敛性，数值实验验证其稳定性与效率。
AI 中文摘要
分裂指数函数和指数类函数可以显著降低指数积分器的总体计算成本，这为其严格分析提供了强有力的动机。本文分析了两个非交换无界算子的分裂误差，并推导了包含流行的Lie-Trotter和Strang情形的新表示。此外，在强连续半群的抽象框架内，我们证明了半线性问题的指数欧拉方法的分裂版本和二阶指数龙格-库塔方法的收敛性。在非线性色散方程和扩散-反应方程上的数值实验展示了所提出的分裂指数积分器相较于现有技术的理论发现、稳定性性质和效率。
英文摘要
Splitting the exponential and exponential-like functions can significantly reduce the overall computational cost of exponential integrators, providing a strong motivation for their rigorous analysis. In this paper, we analyze splitting errors for two noncommuting unbounded operators and derive new representations that include the popular Lie--Trotter and Strang cases. Moreover, within the abstract framework of strongly continuous semigroups, we prove the convergence of a split version of the exponential Euler method and a second-order exponential Runge--Kutta method for semilinear problems. Numerical experiments on a nonlinear dispersive equation and a diffusion--reaction equation demonstrate the theoretical findings, stability properties, and efficiency of the proposed split exponential integrators compared to the state of the art.
