Y'=(1+y^2)cost, with y(0)=0 on the interval [0,6], with h_0=1. For eight step sizes starting with h_0 and halv

y'=(1+y^2)cost, with y(0)=0 on the interval [0,6], with h_0=1. For eight step sizes starting with h_0 and halving each time, find an approximate solution using Euler's method and the Range-Kutta methods of orders 2 and 4.

I already know the exact solution is y(t)=tan(sint)
the values of h are 1, 0.5, 0.25, 0.125... for eight step sizes.

I need to find the approximate solutions of each of these step sizes using each of these three methods. Thank you!

It's Runge-Kutta

If you think anyone is going to go slogging through the entire solutions for you good luck with that thought. I am not.

Say what you've done, say what you can't do. You're expecting someone to put in a good hours work just slogging though the iterations, do it yourself - also think yourself lucky, now you have spreadsheets to do the graft for you, in our day we had to tabulate everything by hand.

Put some brackets in as well, it's not tan(sint) it's tan(sin(t)) and cos(t)

Three methods? You only mention 2 I think. Say what you can't do and I'll check your working, I am not going to do all that for you and I hope noone else does either.

Euler's method however is:

http://en.wikipedia.org/wiki/Euler_metho…
R-T
http://en.wikipedia.org/wiki/Runge%E2%80…