Module V: Numerical solution of ordinary differential equations (ODEs)
Newton mechanics invariably results in (systems of) ODEs describing the motion of a system. When these ODEs are nonlinear, in most cases no explicit solution exists. In this modules we study numerical methods for approximately solving systems of ODEs. We examine the error with respect to the exact solution (as a function of time-step size). We also analyse the stability of the schemes, which descibes the maximum time-step for which a scheme gives a reasonable result.
I made a big mistake here - the Jacobian should have a cosine instead of a sine. The results of forward Euler are unaffected, but the backward Euler should damp the oscillation of the pendulum much more. Will fix with a new video.
