Sufficient conditions for the convergence of the Magnus expansion

Details Sufficient conditions for the convergence of the Magnus expansion Sufficient conditions for the convergence of the Magnus expansion

2007-11-15

arxiv.org/abs/0711.2381v1

J. Phys. A: Math. Theor. 40 (2007), 15001-15017

Mathematics

Classical Analysis and ODEs

20 pages

Scientific paper

10.1088/1751-8113/40/50/006

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.

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