Frequently, as in missile control systems, linear differential equations are simultaneous with nonlinear but slower acting differential equations. The numerical solution of this type of system on a digital computer is significantly speeded up by approximating the forcing functions with polynomials, solving the linear equations exactly, and numerically integrating the nonlinear equations with Milne integration. Automatic interval adjustment is possible by comparing errors in the nonlinear integration. The interval selected is related to the shortest time constant of the nonlinear equations rather than the shortest of all the equations. With this system, both detailed transient response and steady state conditions are revealed with a minimum of machine time.