ODE I
Exercise 3

The resulting energy plots for tau = 0.1 s  and tau = 0.01 s are labeled:
Energy_tau0.1_EC.pdf
Energy_tau0.01_EC.pdf

The results show that the Euler-Cromer method givs significantly better results for the same size time step than the Euler method although the result is quite different. In case the energy oscillates rather than just increasing. But the oscillation give only a peak to peak energy change of about 10% for tau = 0.1 as opposed to climbing to 1927% using the Euler method. For tau = 0.01 s the error still oscillates, but drops to 1%.

For the larger amplitude the oscillations are no longer sinusoidal see the plot Large_Amplitude.pdf). The pendulum slows down considerably at the end of each swing as one would expect since the nearly-horizontal component of the gravitational force that causes the swing is small there. 


