On the Alekseev-Gröbner formula in Banach spaces

Arnulf Jentzen; Felix Lindner; Primož Pušnik

doi:10.3934/dcdsb.2019128

Article Contents

2019, Volume 24, Issue 8: 4475-4511. Doi: 10.3934/dcdsb.2019128

This issue Previous Article On the eventual stability of asymptotically autonomous systems with constraints Next Article Mean-square approximations of Lévy noise driven SDEs with super-linearly growing diffusion and jump coefficients

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
^* Corresponding author: Primož Pušnik

Received: October 31, 2018

Revised: February 28, 2019

Early access: June 2019

Published: July 2019

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 34A99; Secondary: 65L99.

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References

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