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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(t_{old}) +a((u(t_{old})+au(t_{old})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 bya? 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.

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# Heun's method question

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