On monodromy matrix computation Original Research Article

We present a study on the critical time step for the numerical integration based on the Runge–Kutta 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 Lyapunov–Schmidt 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.