Estimating the convergence rate $r$

Perform numerical experiments: $(\Delta t_i, E_i)$, $i=0,\ldots,m-1$. Two methods for finding $r$ (and $C$):

1. Take the logarithm of (1), $\ln E = r\ln \Delta t + \ln C$, and fit a straight line to the data points $(\Delta t_i, E_i)$, $i=0,\ldots,m-1$.
2. Consider two consecutive experiments, $(\Delta t_i, E_i)$ and $(\Delta t_{i-1}, E_{i-1})$. Dividing the equation $E_{i-1}=C\Delta t_{i-1}^r$ by $E_{i}=C\Delta t_{i}^r$ and solving for $r$ yields

Method 2 is best.