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Heun's method question

  1. Oct 17, 2015 #1
    Hi there,

    in my notes for Heun's method for solving an ODE, I have

    y(new) = y(old) + 0.5(k1 + k2)Δh

    And k1 is supposed to be f(y(old)) while k2 is f(y(old) + q11k1Δh) and q11 is 1

    So if for example I have a simple differential equation like du/dt = au

    It would be du/dt = 0.5(k1 + k2)

    du/dt = 0.5(au(told) + a((u(told)+au(told)Δt))

    The first term on the right of the equal is k1, and the term after is k2. What I don't understand is why the entire k2 term is multiplied by a? It's not in any formula so what mistake have I made here. I couldn't really find this in any of my books either, especially since the notation is so different.
     
  2. jcsd
  3. Oct 17, 2015 #2
    I figured it out. This thread can be deleted.
     
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