Checking convergence rates

The next function estimates convergence rates, i.e., it

• performs $m$ simulations with halved time steps: $2^{-k}\Delta t$, $k=0,\ldots,m-1$,
• computes the $L_2$ norm of the error, $E = \sqrt{\Delta t_i\sum_{n=0}^{N_t-1}(u^n-\uex(t_n))^2}$ in each case,
• estimates the rates $r_i$ from two consecutive experiments $(\Delta t_{i-1}, E_{i-1})$ and $(\Delta t_{i}, E_{i})$, assuming $E_i=C\Delta t_i^{r_i}$ and $E_{i-1}=C\Delta t_{i-1}^{r_i}$: