常微分方程组数值求解的反馈镇定方法
Feedback Stabilization Methods for the Numerical Solution of Systems of Ordinary Differential Equations
AI总结：
利用非线性控制理论中的Lyapunov和小增益反馈镇定方法，研究保证数值解与原始常微分方程组定性行为一致的步长选择问题，并应用于全局离散误差控制。
摘要：
本文利用非线性控制理论的工具，研究数值格式的步长选择问题，以保证数值解呈现与原始常微分方程组相同的定性行为。我们利用了基于Lyapunov和小增益的反馈镇定方法，并对具有全局渐近稳定平衡点的系统给出了大量说明性应用。所得结果也可用于控制全局离散误差。
英文摘要：
In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools from nonlinear control theory. Lyapunov-based and Small-Gain feedback stabilization methods are exploited and numerous illustrating applications are presented for systems with a globally asymptotically stable equilibrium point. The obtained results can be used for the control of the global discretization error as well.
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