On monodromy matrix computation
We present a study on the critical time step for the numerical integration based on the RungeKutta method of the monodromy matrix (the fundamental matrix solution) associated with a set of n first-order linear ordinary differential equations with periodic coefficients. By applying the LyapunovSchmidt method, for any dimension n and systems which are perturbations of autonomous systems, we give an approximation to the critical time step which involves the autonomous part as well as the periodic perturbations.
instability analysis floquet monodromy analysis