HW2 problems?

[CM]

I see that E2.1(a) is assigned.  There's no 2.1(a), though.  Did you mean 2.1, or 2.2(a)?

[Jay Wang]

There is a slight difference here between the lecture notes (draft) and the book.
If you are referring to the book, it should be E2.2 (a).
On the manuscript notes, it is E2.1(a)

[CM]

This question wants us to show second order accuracy, and the equivalence of 2 different RK2 methods.  Is it sufficient to demonstrate accuracy and equivalence by numerically solving an ODE?  Or are you looking for a traditional proof?

[Jay Wang]

 It's asking for an analytic proof. Expand k2 in powers of h, and show that the error is of the order h^3.
If you like, you may assume explicit dependence on t of the derivative f(t) to make it easier.

Of course, it'd be complete if you test this to be true numerically too (not required).