I found this question extremely difficult... Especially part b. For part b, I've tried several times. Is it correct that we need to use Taylor expansion to solve it?
Since $e'(t) = f(...) + u'(t)$, we just use Lagrange polynomial interpolation to find the $u(t)$, and then take the derivative of u, so that we could have $u'(t)$.
And then for $e_n+1 = e_n(==0) + h*(f(...) ) - h * u'(t_n)$. Then we go back to the $u'(t)$ function, and calculate for $u'(tn)$?
After we have $e_n+1$, we could calculage $e_n+2$, like $e_n+2 = e_n+1 + h *f(...) - h * u'(t_n+1)$?
Is it a way that could work?
Thanks for the help!