Solve the equation

$\frac{d}{dt}=\frac{-2{}^3}{t+},(0)=1$

numerically on the interval $0t1$ using a time step $t=0\mathrm{.}5$ by the Crank Nicolson method. $($b$)$ By approximately what factor would you expect the error in $(1)$ to be reduced if the time step were halved?