Numerical solution of state equations

A relationship is noted between solutions of state equations obtained by numerical computation of the matrix exponential e^ATand solutions obtained using standard numerical integration techniques. The Runge-Kutta methods are shown to be equivalent to the series expansion e^ATout to fixed number of terms, depending on the order of the particular Runge-Kutta method used. As a result of this relationship one can see how highly efficient numerical integration routines may be written for a large class of dynamical systems.