1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Proving a R-K method's order

  1. Dec 8, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]k_2=f(t_n+2h/3,x_n+2h k_1/3)[/tex]
    [tex]x_{n+1}=x_n + h(k_1+ k_2+2k_3)/4[/tex]

    Prove that the above Runge-Kutta method is of third order by examining the problem
    [tex]x'=x, \; x(0)=1[/tex].

    2. Relevant equations

    3. The attempt at a solution
    I have to prove that the difference between the exact solution (which is exp(x)) and the solution given by the RK is of magnitude h4, where h is the step size. I'm just being very thick-skulled here, I can program this in Matlab but I can't do it on paper.
    Can someone just show me how I calculate k1, k2 and k3? I don't completely understand the notation used. What is f(tn,xn)?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted