I don't understand how to find the correct step-size $h$ for the Euler method. My script says the following:
One method consists in computing the numerical solution for an arbitrary $h$ and then $2h$. The Richardson extrapolation gives an estimate of $e = \max_t|y(t,2h)-y(t,h)|$ of the error. When the error is smaller than the tolerance, we keep the result and start from $2y(t,h)-y(t,h)$. If the error is larger we restart with $h/2$ until we reach the tolerance.
( $y(t,2h)$ means approximation with $2h$)
I don't understand why the Richardson extrapolation is mentioned. For what do I have to use it? Can I not just calculate $y(t,2h)$ and $y(t,h)$ and see the error?