Example Code

• import numpy as np
• from scipy.integrate import odeint
• import matplotlib.pyplot as plt
• def dU_dx(U, t):
•       k=-1;
•       return [U[1], -1*U[1]-100*U[0]]
• U0 = [10, 0]
• xs = np.linspace(0, 10, 5000)
• Us = odeint(dU_dx, U0, xs)
• ys = Us[:,0]
• plt.xlabel("t")
• plt.ylabel("x")
• plt.title("Damped harmonic oscillator")
• plt.plot(xs,ys);
• plt.show()

Note and Comments

• import numpy as np: 讀入numpy函式庫並命名為np
• from scipy.integrate import odeint 讀取scipy.integrate函式庫的odeint函式庫 (可使用odeint求解ODE)
• def model(I,t): 定義常微分方程式
•       k = 1
•       dIdt = -k * I
•       return dIdt
• I0 = 1 設定I(t)在t=0的初始值
• I = odeint(model, I0, t): odeeint() 爲解常微分方程的求解程式, 其中第一個變量equation是我們求欲求解的常微分方程, I0爲初始值, t爲變數

result