In this lecture we deepened our understanding of numerical methods for
solving ordinary differential equations by applying these techniques
to the classical example of particle motion. This example involves,
as usual for Newtonian mechanics, second order derivatives by equating
the acceleration of a body with the force acting on it, scaled by the
mass. Although at first sight this form of a differential equation
did not fit the methods developed up to then, we were able to rewrite
the equation of motion in a form suitable for treating with the
Euler method.
After gaining some further insight into the origin of the error inherent
to this and all other methods we discussed two versions of the
Runge-Kutta method, a standard method for solving
differential equations.