Radioactivity exponential decay 指數衰減 dy/dt= -ky
Example Code
- import numpy as np
- from scipy.integrate import odeint
- import matplotlib.pyplot as plt
- def model(I,t):
- k = 1
- dIdt = -k * I
- return dIdt
- I0 = 1
- t = np.linspace(0, 5)
- I = odeint(model, I0, t)
- plt.plot(t,I)
- plt.title('Exponential decay');
- plt.text(1.7, 0.8, r'$\frac{dI}{dt} = -kI$ with initial value k=1;', fontsize=18)
- plt.text(1.7, 0.7, r'solution: I(t)=Ie$^{-kI}$.', fontsize=18)
- plt.xlabel('time')
- plt.ylabel('I(t)')
- 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