随机单对角隐式龙格-库塔方法的误差界与稳定性分析
Error Bound and Stability Analysis for a Randomized Singly Diagonally Implicit Runge-Kutta Method
AI总结：
研究基于随机梯形法则的随机SDIRK方法，证明其在低正则性假设下均方根意义下以2.5阶收敛，通过数值实验展示该方法应用于非光滑问题时的鲁棒性。
AI中文摘要：
本文提出一种基于随机梯形法则的随机单对角隐式龙格-库塔（SDIRK）方法。该方法的每个实现都是至少二阶的代数稳定SDIRK方法。主要结果证明了在低正则性假设下，随机方案在均方根意义下以2.5阶收敛。数值实验说明了新方案应用于非光滑问题时的鲁棒性。
英文摘要：
A randomized Singly Diagonally Implicit Runge-Kutta (SDIRK) method, based on the randomized trapezoidal rule as the underlying quadrature scheme, is proposed. Every realization of the scheme is an algebraically stable SDIRK method of at least second order. The main result is the proof that the randomized scheme converges with order 2.5 in the root mean square sense under low regularity assumptions. Numerical experiments illustrate the robustness of the new scheme when applied to nonsmooth problems.
