  A numerical technique used to solve boundary value problems is modified to
find periodic steady-state solutions of nonautonomous dynamical systems. The
technique uses a matrix representation of the time derivative obtained through
trigonometric interpolation of a periodic function. Such a differentiation
matrix yields exact values for the derivative of a trigonometric polynomial and
therefore, can be used as the main ingredient of a numerical method to solve
nonlinear dynamical systems. We apply this technique to obtain some limit
cycles and bifurcation points of a sinusoidally driven pendulum and the
steady-state response of an electric circuit.
