Question

Could anyone help me understand how to read Butcher tableau?

https://en.wikipedia.org/wiki/List_of_Runge%E2%80%93Kutta_methods

It seems very unintuitive to me

Answer 1

I am unable to find any well put together tutorials for how to read these online, or rather acquire the formulas from them

Answer 2

I understand this now it isn't so bad

Answer 3

you just go row by row, each row represents a k value so the top row is k1

For huen's
by the first row
k1 = f(x, y)
by the second row
k2 = f(x + h, y + h(k1))

Then when you get to the bottom you take the sum of all of the k1s and multiply them by their corresponding c value then plug that into the bottom equation and you get:

yi + (1/2)(f(y, x)+f(x + h, y + h(k1)))h

as you can see you can see its the same as the forum you normally see:
y + h(k1) = yi + f(x,y)h = y^(o)

yi + (1/2)(f(y, x)+f(x + h, y^o))h

Answer 4

Try:
https://www.math.auckland.ac.nz/~butcher/ODE-book-2008/Tutorials/RK-methods.pdf