(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]x'=f(t,x)[/tex]

[tex]k_1=f(t_n,x_n)[/tex]

[tex]k_2=f(t_n+2h/3,x_n+2h k_1/3)[/tex]

[tex]k_3=f(t_n+2h/3,x_n+h(k_1+3k_2)/6[/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 h^{4}, 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 k_{1}, k_{2}and k_{3}? I don't completely understand the notation used. What is f(t_{n},x_{n})?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**