Solve the following ODE analytically
$\displaystyle \dfrac{d^2 \theta}{dt^2}=-\dfrac{g}{l}\sin{\theta}$
If I remember rightly, the solution can only be found using the Airy function. Are you familiar with it?
Edit: In fact, the solution is written in terms of Elliptic integrals. Are you familiar with them? You will find the solution discussed in any decent textbook on nonlinear differential equations (many of which are likely to be in the library of the institute you study at).