On the Alekseev-Gröbner formula in Banach spaces

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.

36 pages

References in corpus (1)

• Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations

Cited by in corpus (2)

• High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations
• Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noise