Solutions of ordinary differential equations (2) examples

use SciPyのscipy.integrate.odeint Solve simultaneous differential equations , In time t（tの The scope is 0~ Just a few seconds , example ：t=0~2 second ） Reconciliation x(t), y(t), z(t) Make a picture .

 

As t=0 Initial conditions of ,x(t=0) = -10, y (t=0) = 0, z (t=0) = 35.0. also , About the coefficient a,b,c, You can try a = 40, b = 5, c = 35 And a = 40, b = 10, c = 35 The situation of . And time division Δt Take a smaller value appropriately . in addition ,Δt If it is too small , The amount of calculation will become very large . Adjust according to the errors after the actual implementation .

Here are the solutions python Program ：

import numpy as np
import scipy.integrate as sciin
import matplotlib.pyplot as plt

# Compare with the independent variable t The function name of the related derivative function is placed in F in 
def f(F, t,params):    
    x,y,z = F       
    f_values = [a*(y-x),(c-a)*x-x*z+c*y,x*y-b*z]   # Write separately x,y,z The derivative of is equal to the formula on the right of  
    return f_values


#  Amplification coefficient 
a = 40           
b= 5                
c = 35       
# Put the above three coefficients into parameters in 
parameters = [a,b,c]

# Set up x,y,z The initial value of the 
x0 = -10      
y0 = 0.0  
z0 = 35  
#　 Put the initial value into Y0 in 
Y0 = [x0,y0,z0]

#  Starting point , The end point , Interval setting 
tStart = 0.0        
tStop  = 2   
tInc   = 0.01       # interval 
# Summarize the above to t in 
t = np.arange(tStart, tStop, tInc)

# sciin.odeint Explain ODE
solution = sciin.odeint(f, Y0, t, args=(parameters,))

#  Make a picture 
plt.figure(figsize=(9.5, 6.5))
plt.plot(t, solution[:, 0], color='black')
plt.plot(t, solution[:, 1], color='green')
plt.plot(t, solution[:, 2], color='red')
plt.xlabel('time, t' , fontsize=14)
plt.ylabel('theta(t)', fontsize=14)
plt.show()

  I'm a genius .