# The application of Matplotlib in solving ordinary differential equation of Python 3 SCI

Keywords: jupyter Python IPython Anaconda

Python scientific calculation simply records several notes, uses SciPy to solve ordinary differential equations, and uses matplotlib to demonstrate in jupyter notebook. The following points need to be noted:

• odeint function provided by integration module
• On jupyter notebook of Anaconda 3
• matplotlib 2D drawing to solve Newton's cooling law
• Solving Lorentz attractor with matplotlib 3D rendering

#### Drawing 2D chart on jupyter notebook

%matplotlib inline #Inline display
# %config InlineBackend.figure_format="svg" #Display on Web page in svg format
import numpy as np
import matplotlib.pyplot as plt

x1 = np.linspace(0.0, 5.0)
x2 = np.linspace(0.0, 2.0)

y1 = np.cos(2 * np.pi * x1) * np.exp(-x1)
y2 = np.cos(2 * np.pi * x2)

plt.subplot(2, 1, 1)
plt.plot(x1, y1, '.-')
plt.title('A tale of 2 subplots')
plt.ylabel('Damped oscillation')

plt.subplot(2, 1, 2)
plt.plot(x2, y2, '-')
plt.xlabel('time (s)')
plt.ylabel('Undamped')

#### T′(t)=−α(T(t)−H)T(t)=H+(T0−H)e−αtT′(t)=−α(T(t)−H)T(t)=H+(T0−H)e−αt

%matplotlib inline
from scipy.integrate import odeint
import matplotlib.pyplot as plt
import numpy as np

from IPython import display

# Differential equation of cooling law
def cooling_law_equ(w, t, a, H):
return -1 * a * (w - H)

# The function of temp erature obtained by cooling law with respect to time t
def cooling_law_func(t, a, H, T0):
return H + (T0 - H) * np.e ** (-a * t)

t = np.arange(0, 10, 0.01)
initial_temp = (90) #initial temperature
temp = odeint(cooling_law_equ, initial_temp, t, args=(0.5, 30)) #Cooling coefficient and ambient temperature
temp1 = cooling_law_func(t, 0.5, 30, initial_temp) #Comparison between the derived function and the result of scipy calculation
plt.subplot(2, 1, 1)
plt.plot(t, temp)
plt.ylabel("temperature")

plt.subplot(2, 1, 2)
plt.plot(t, temp1)
plt.xlabel("time")
plt.ylabel("temperature")

display.Latex("Newton's law of cooling $T'(t)=-a(T(t)- H)$)(Upper) sum $T(t)=H+(T_0-H)e^{-at}$(Next)")

#### Drawing 3D charts on jupyter notebook

%matplotlib inline
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt

mpl.rcParams['legend.fontsize'] = 10

fig = plt.figure()
ax = fig.gca(projection='3d')
theta = np.linspace(-4 * np.pi, 4 * np.pi, 100)
z = np.linspace(-2, 2, 100)
r = z**2 + 1
x = r * np.sin(theta)
y = r * np.cos(theta)
ax.plot(x, y, z, label='parametric curve')
ax.legend()

#### Demonstration of Lorentz attractor in three dimensional space

dxdt=σ⋅(y−x)dydt=x⋅(ρ−z)−ydzdt=xy−βzdxdt=σ⋅(y−x)dydt=x⋅(ρ−z)−ydzdt=xy−βz

%matplotlib inline
from scipy.integrate import odeint
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt

from IPython import display

fig = plt.figure()
ax = fig.gca(projection='3d')

def lorenz(w, t, p, r, b):
# Position vector w, three parameters p, r, b
x, y ,z = w.tolist()
# Calculate dx/dt, dy/dt, dz/dt respectively
return p * (y-x), x*(r-z)-y, x*y-b*z

t = np.arange(0, 30, 0.02)
initial_val = (0.0, 1.00, 0.0)

track = odeint(lorenz, initial_val, t, args=(10.0, 28.0, 3.0))
X, Y, Z = track[:,0], track[:,1], track[:,2]
ax.plot(X, Y, Z, label='lorenz')
ax.legend()

display.Latex(r"$\frac{dx}{dt}=\sigma\cdot(y-x) \\ \frac{dy}{dt}=x\cdot(\rho-z)-y \\ \frac{dz}{dt}=xy-\beta z$")

Copyright notice: This is the original article of the blogger. It can't be reproduced without the permission of the blogger. https://blog.csdn.net/m454078356/article/details/77776092

Article label: python

Personal classification: Python

Related hot words: python3∑ python3 python3 and python3 package python3 Library

Posted by phpcodec on Thu, 13 Feb 2020 12:52:36 -0800