2. (5 points) Do the same thing as in the previous problem, but now
include the fourth-order Runge-Kutta method (that you have written
yourself) as well. In this problem, treat the fourth-order Runge-Kutta
solution with $n = 10^5$ as the true solution. Also, in addition to plotting
the $\log_{10}$ of the errors (i.e., $|y_n - \hat{y}(t_n)|$) versus the $\log_{10}(n)$, plot the $\log_{10}$
of the errors versus the $\log_{10}$ of the number of function evaluations (i.e.,
1
the number of times that you evaluated $f(t, y)$) for each method. Has
this changed the slopes compared with the plot where the horizontal
axis was the number of steps ($\log_{10}(n)$)?
3. (3 points) Do the same thing as in the previous problem, but now
include Euler's method. From the log-log plot, estimate the error in
Euler's method with $n = 1000$ steps.
