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Math Help - Verifying the order of a Runge-Kutta method

  1. #1
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    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?
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  2. #2
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    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".
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    Re: Verifying the order of a Runge-Kutta method

    Quote Originally Posted by phys251 View Post
    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
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