On the Alekseev-Gr\"obner formula in Banach spaces
Arnulf Jentzen, Felix Lindner, Primo\v{z} Pu\v{s}nik
TL;DR
This paper extends the Alekseev-Gröbner formula, a key tool in numerical analysis, to Banach space valued ODEs under mild perturbation conditions, broadening its applicability.
Contribution
It provides a novel extension of the Alekseev-Gröbner formula specifically for Banach space valued ODEs, under mild assumptions on perturbations.
Findings
Extended the formula to Banach spaces
Applicable under mild perturbation conditions
Enhances analysis of Banach space ODEs
Abstract
The Alekseev-Gr\"obner formula is a well known tool in numerical analysis for describing the effect that a perturbation of an ordinary differential equation (ODE) has on its solution. In this article we provide an extension of the Alekseev-Gr\"obner formula for Banach space valued ODEs under, loosely speaking, mild conditions on the perturbation of the considered ODEs.
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