Sensitivity of ODE Solutions and Quantities of Interest with Respect to Component Functions in the Dynamics

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-10-09 DOI:10.1137/25m1729563

Jonathan R. Cangelosi, Matthias Heinkenschloss

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Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 5, Page 2094-2118, October 2025.
Abstract. This work analyzes the sensitivities of the solution of a system of ordinary differential equations (ODEs) and a corresponding quantity of interest (QoI) to perturbations in a state-dependent component function that appears in the governing ODEs. This extends existing ODE sensitivity results, which consider the sensitivity of the ODE solution with respect to state-independent parameters. It is shown that with Carathéodory-type assumptions on the ODEs, the implicit function theorem can be applied to establish continuous Fréchet differentiability of the ODE solution with respect to the component function. These sensitivities are used to develop new estimates for the change in the ODE solution or QoI when the component function is perturbed. In applications, this new sensitivity-based bound on the ODE solution or QoI error is often much tighter than classical Gronwall-type error bounds. The sensitivity-based error bounds are applied to a trajectory simulation for a hypersonic vehicle.

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动力学中关于分量函数的ODE解的灵敏度和感兴趣的量

SIAM数值分析杂志，第63卷，第5期，2094-2118页，2025年10月。摘要。本工作分析了常微分方程（ode）系统的解的敏感性和相应的兴趣量（qi）对出现在控制ode中的状态相关分量函数中的扰动的敏感性。这扩展了现有的ODE灵敏度结果，这些结果考虑了ODE解决方案相对于状态无关参数的灵敏度。证明了在对ODE的carathacemody型假设下，隐函数定理可用于建立ODE解对分量函数的连续fracemody可微性。当组件功能受到干扰时，这些灵敏度用于为ODE解决方案或qi中的变化开发新的估计。在应用程序中，这种新的基于灵敏度的ODE解决方案或QoI错误边界通常比经典的gronwall型错误边界要严格得多。将基于灵敏度的误差界应用于高超声速飞行器的弹道仿真。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.