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arXiv 2209.074822022-09math.NAcs.NA

非精确信息下非线性常微分方程解近似的 Euler 格式

Euler scheme for approximation of solution of nonlinear ODEs under inexact information

Natalia Czyżewska, Paweł M. Morkisz, Paweł Przybyłowicz

备注：: 18 pages, 9 figures
DOI：: 10.1016/j.apnum.2023.08.002

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AI总结：

针对右端函数满足局部单侧 Lipschitz 与 Hölder 条件且信息可能含噪的非线性 ODE，本文分析 Euler 格式的误差与最优性，并通过数值实验验证。

摘要：

我们研究 Euler 格式的误差，此时底层 ODE 的右端函数满足局部单侧 Lipschitz 条件和局部 Hölder 连续性等非标准假设。此外，关于信息可得性，我们假设右端函数存在两种情形：精确信息与含噪信息。文中还给出了 Euler 格式的最优性分析。最后，我们展示了若干数值实验的结果。

英文摘要：

We investigate error of the Euler scheme in the case when the right-hand side function of the underlying ODE satisfies nonstandard assumptions such as local one-sided Lipschitz condition and local Hölder continuity. Moreover, we assume two cases in regards to information availability: exact and noisy with respect to the right-hand side function. Optimality analysis of the Euler scheme is also provided. Finally, we present the results of some numerical experiments.

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