Verifying the order of a Runge-Kutta method

I am to verify that the following one-step RK3:

Phi(x, y; h) = (k1 + 4k2 + k3)/6,

k1 = f(x, y)

k2 = f(x + h/2, y + h/2 * k1)

k3 = f(x + h, y + h(-k1 + 2k2))

Is third-order.

My prof showed me how to do this, but I got overwhelmed quickly. Is there a resource, website, video, etc. that can show me how to do this sort of thing in step-by-step detail?

Re: Verifying the order of a Runge-Kutta method

What do **you** mean by "third order". I would be inclined to say that this algorithm uses the value of f at three difference points, (x, y), (x+ h/2, x+ h/2*k1), and (x+ h, y+ h(-k1+ 2k2)) and so is "third order" but you appear to have a different definition of "order".

Re: Verifying the order of a Runge-Kutta method

Quote:

Originally Posted by

**phys251** I am to verify that the following one-step RK3:

Phi(x, y; h) = (k1 + 4k2 + k3)/6,

k1 = f(x, y)

k2 = f(x + h/2, y + h/2 * k1)

k3 = f(x + h, y + h(-k1 + 2k2))

Is third-order.

My prof showed me how to do this, but I got overwhelmed quickly. Is there a resource, website, video, etc. that can show me how to do this sort of thing in step-by-step detail?

Numerical analysis textbooks usually discuss this in detail, see if this link could help Runge-Kutta Methods