lorenzSoluce.py
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#
# PYTHON for DUMMIES
# Probleme 5
#
# Solution detaillée
# Vincent Legat
#
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from numpy import *
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# -1- Equations de Lorenz avec les paramètres de l'énoncé
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#
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# dudt(t) = 10 v(t) - 10 u(t)
# dvdt(t) = 28 u(t) - v(t) - u(t)w(t)
# dwdt(t) = u(t) v(t) - 8 w(t) / 3
#
#
def f(x,u):
dudt = 10 * u[1] - 10 * u[0]
dvdt = 28 * u[0] - u[1] - u[0] * u[2]
dwdt = u[0] * u[1] - 8 * u[2] / 3
return array([dudt,dvdt,dwdt])
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#
# -2- Schema de Runge-Kutta classique d'ordre 4
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def lorenz(Xstart,Xend,Ustart,n):
X = linspace(Xstart,Xend,n+1)
U = zeros((n+1,3)); U[0,:] = Ustart
h = (Xend - Xstart)/n
for i in range(n):
K1 = f(X[i] ,U[i,:] )
K2 = f(X[i]+h/2,U[i,:]+K1*h/2)
K3 = f(X[i]+h/2,U[i,:]+K2*h/2)
K4 = f(X[i]+h ,U[i,:]+K3*h )
U[i+1,:] = U[i,:] + h*(K1+2*K2+2*K3+K4)/6
return X,U
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