The chosen scheme

The equation of the pendulum is :

that is to say, the following problem to solve :

These equations are discretised by this way :To see the effects of the different schemes (Euler, Runge-Kutta 4), a simple pendulum (undamped and undriven) was used.It is an Euler scheme, which is explicit for the first equation, and implicit for the second. This has been chosen, because a simple explicit scheme was not efficient enough.