# How to derive the Runge Kutta 2nd Order Method?

• Oct 10th 2010, 03:33 PM
chutsu
How to derive the Runge Kutta 2nd Order Method?
I understand that the Runge Kutta is simply an extension of the Euler Method, which is:

$y_{i+1} = y_i + f(x,y)h+\frac{1}{2!}f'(x,y)h^2$

But then I don't see how to get $k_1$ and $k_2$? Also in some text books, what does this partial derivative mean?

$\frac{\partial{y}}{\partial{x}}|_{x_i, y_i}$

What is up with the vertical bar and the variables at the bottom?

Thanks