# American Institute of Mathematical Sciences

August  2019, 24(8): 4475-4511. doi: 10.3934/dcdsb.2019128

## On the Alekseev-Gröbner formula in Banach spaces

 1 Seminar for Applied Mathematics, Department of Mathematics, ETH Zürich, Zürich, Switzerland 2 Institute of Mathematics, Faculty of Mathematics and Natural Sciences, University of Kassel, Kassel, Germany

* Corresponding author: Primož Pušnik

This paper is dedicated to Peter Kloeden on the occasion of his 70th birthday

Received  November 2018 Revised  March 2019 Published  June 2019

Fund Project: This work was partially supported by the SNSF-Research project 200021_156603 "Numerical approximations of nonlinear stochastic ordinary and partial differential equations"

The Alekseev-Gröbner 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-Gröbner formula for Banach space valued ODEs under, loosely speaking, mild conditions on the perturbation of the considered ODEs.

Citation: Arnulf Jentzen, Felix Lindner, Primož Pušnik. On the Alekseev-Gröbner formula in Banach spaces. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 4475-4511. doi: 10.3934/dcdsb.2019128
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