Rungge Kutta Method
7
y(t) f (y, t) = dy dt y(t + h) = y (t) + 1 6 · (k 1 + 2 k 2 + 2 k 3 + k 4 ) (1) k 1 = h · f (t, y) (2) k 2 = h · f (t + h 2 , y(t) + k 1 2 ) (3) k 3 = h · f (t + h 2 , y(t) + k 2 2 ) (4) k 4 = h · f (t + h, y(t) + k 3 ) (5) m dv dt = −mg − bv 2 (6) dx dt = v (7) m v g b x g v x v b b = 1 2 (C d A)ρ (8) C d A ρ ρ ρ = ρ 0 e −h h 0 (9) ρ 0 h h 0
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Transcript of Rungge Kutta Method
8/10/2019 Rungge Kutta Method
http://slidepdf.com/reader/full/rungge-kutta-method 1/7
y(t) f (y, t) = dydt
y(t + h) = y(t) + 1
6 · (k1 + 2k2 + 2k3 + k4) (1)
k1 = h · f (t, y) (2)
k2 = h · f (t + h
2, y(t) +
k1
2 ) (3)
k3 = h · f (t + h
2, y(t) +
k2
2 ) (4)
k4 = h · f (t + h, y(t) + k3) (5)
mdvdt = −mg − bv2 (6)
dx
dt = v (7)
m v g b
x
g v x
v
b
b = 1
2(C dA)ρ (8)
C d A ρ
ρ
ρ = ρ0e−h
h0 (9)
ρ0 h h0
8/10/2019 Rungge Kutta Method
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8/10/2019 Rungge Kutta Method
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±n
8/10/2019 Rungge Kutta Method
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±n
45
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< 45
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