  We present three alternative derivations of the method of characteristics
(MOC) for a second order nonlinear hyperbolic partial differential equation.
The MOC gives rise to two mutually coupled systems of ordinary differential
equations. As a special case we consider the Monge-Amp\`ere equation, for which
we solve the system of ODE's using explicit one-step methods (Euler,
Runge-Kutta) and spline interpolation. Numerical examples demonstrate the
performance of the methods.
