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.Comment: 36 page
