Sufficient conditions for the convergence of the Magnus expansion

Fernando Casas

Published 2007-11-15Version 1

Two different sufficient conditions are given for the convergence of the Magnus expansion arising in the study of the linear differential equation $Y' = A(t) Y$. The first one provides a bound on the convergence domain based on the norm of the operator $A(t)$. The second condition links the convergence of the expansion with the structure of the spectrum of $Y(t)$, thus yielding a more precise characterization. Several examples are proposed to illustrate the main issues involved and the information on the convergence domain provided by both conditions.