Modellering i Tidsplanet
Modellering i Tidsplanet
Modellering i Tidsplanet
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Faltning Differensekvationer Differentialekvationer<br />
Approximation av andra-derivator<br />
Euler-approximation of första-derivata<br />
dy(t)<br />
y(nT + T ) − y(nT )<br />
dt ∣ ≈<br />
t=nT<br />
T<br />
Euler-approximation av andra-derivata<br />
=<br />
y[n + 1] − y[n]<br />
T<br />
d 2 y(t)<br />
dt 2<br />
=<br />
∣<br />
∣∣t=nT<br />
≈ dy<br />
dt | t=nT +T − dy<br />
dt | t=nT<br />
T<br />
(y[n+2]−y[n+1])/T −(y[n+1]−y[n])/T<br />
T<br />
= y[n+2]−2y[n+1]+y[n]<br />
T 2
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