This simple example on solving ordinary differential equations tests
Runke-Kutta method with adaptive step size by solving "simple pendulum"
problem.

It starts pendulum with energy equal E=1 and initial nonzero velocity and
zero position. Time evolution of 200 time-units with is
monitored and the error is printed as well as the energy of the system versus
time. Energy is here slightly increasing - a signature of the degradation.