# 4th order runge kutta method

I just need to know the general form of the 4th order Runge-Kutta method?
For two coupled first order linear ODEs.
I can not find it specifically written online, I need it to write a program for the structure of white dwarfs stars, but I am okay with the Physics, just I have never used the runge-Kutta method.

Thanks.

Related Calculus and Beyond Homework Help News on Phys.org
Filip Larsen
Gold Member
Welcome to PF!

Searching your references for "Runge Kutta 4", or simply "RK4", should provide you with equations that you very easily can turn into a program. If you are not supposed to implement the method yourself, then searching for both RK4 and your favorite language at the same time may even provide you with a code snippet.

For one ODE:

To approximate the solution of the initial-value problem
y' = f(t, y), a <t <b, y(a) = y0,
at (N + 1) equally spaced numbers in the interval [a,b]:
INPUT endpoints a, b; integer N; initial condition y0.
OUTPUT approximation w to y at the (N + 1) values of t.
Step 1 Set h = (b - a)/N;
t = a;
w = y0;
OUTPUT (t, w).
Step 2 For i = 1, 2,... , N do Steps 3-5.
Step 3 Set K1=hf(t,w);
K2 = hf(t + h/2,w + K1 /2);
K3 = hf(t+h/2,w + K2/2);
K4 = hf(t + h,w + K3).
Step 4 Set w = w + (K1 + 2K2 + 2K3 + K4)/6; (Compute w_i)
t = a + ih. (Compute t_i)
Step 5 OUTPUT (t, w).