Alekseev–Gröbner formula
The Alekseev–Gröbner formula, or nonlinear variation-of-constants formula, is a generalization of the linear variation of constants formula which was proven independently by Wolfgang Gröbner in 1960 and Vladimir Mikhailovich Alekseev in 1961. It expresses the global error of a perturbation in terms of the local error and has many applications for studying perturbations of ordinary differential equations. Formulation 

Let  be a natural number, let  be a positive real number, and let  be a function which is continuous on the time interval  and continuously differentiable on the -dimensional space . Let ,  be a continuous solution of the integral equation

Furthermore, let  be continuously differentiable. We view  as the unperturbed function, and  as the perturbed function. Then it holds that

The Alekseev–Gröbner formula allows to express the global error  in terms of the local error . The Itô–Alekseev–Gröbner formula 

The Itô–Alekseev–Gröbner formula is a generalization of the Alekseev–Gröbner formula which states in the deterministic case, that for a continuously differentiable function  it holds that

References 

Nonlinear algebra
Ordinary differential equations