标题： 基于稳定多速率显式格式的奇异摄动系统高效仿真 显示英文标题

标题： Efficient Simulation of Singularly Perturbed Systems Using a Stabilized Multirate Explicit Scheme

摘要： 奇异摄动系统（SPSs）在工程应用中很常见，由于多时间尺度导致的刚性问题，求解其初值问题（IVPs）具有挑战性。 经典的显式方法需要极小的时间步长以保证稳定性，而针对SPSs开发的隐式方法计算成本高且对于强非线性系统效率较低。 本文介绍了一种稳定的多速率显式格式（SMES），它稳定了经典显式方法，而无需使用小时间步长或隐式公式。 通过采用带可变时间步长的多速率方法，SMES允许快速动态迅速收敛到其平衡流形，而慢动态则以更大的步长演化。 分析表明，SMES以显著减少的计算努力和受控误差实现数值稳定性。 其有效性通过一个数值例子进行了说明。 显示英文摘要

摘要： Singularly perturbed systems (SPSs) are prevalent in engineering applications, where numerically solving their initial value problems (IVPs) is challenging due to stiffness arising from multiple time scales. Classical explicit methods require impractically small time steps for stability, while implicit methods developed for SPSs are computationally intensive and less efficient for strongly nonlinear systems. This paper introduces a Stabilized Multirate Explicit Scheme (SMES) that stabilizes classical explicit methods without the need for small time steps or implicit formulations. By employing a multirate approach with variable time steps, SMES allows the fast dynamics to rapidly converge to their equilibrium manifold while slow dynamics evolve with larger steps. Analysis shows that SMES achieves numerical stability with significantly reduced computational effort and controlled error. Its effectiveness is illustrated with a numerical example.