lorenzSoluce.py

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#
# PYTHON for DUMMIES 19-20
# 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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#
#
#           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
# 
  
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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