More about similarities between Runge-Kutta and matrix exponential methods for evaluating transient response

A strict relationship is shown to hold between the Nth-order Runge-Kutta and the Nth-power-retained matrix exponential (Liou´s method) for obtaining the transient response of time-invariant linear systems. Previous results are used to obtain statements of propagated integration error for any order Runge-Kutta when applied to such systems.