```python
```python
import numpy as np
from scipy.integrate import odeint
from matplotlib import pyplot as plt
import os
#先從odeint函數直接求解微分方程
#創建歐拉法的類
class Euler:
#構造方法，當創建對象的時候，自動執行的函數
def __init__(self,h,y0):
#將對象與對象的屬性綁在一起
self.h = h
self.y0 = y0
self.y = y0
self.n = 1/self.h
self.x = 0
self.list = [1]
#歐拉法用list列表,其x用y疊加儲存
self.list2 = [1]
self.y1 = y0
#改進歐拉法用list2列表，其x用y1疊加儲存
self.list3 = [1]
self.y2 = y0
#隱式梯形法用list3列表，其x用y2疊加儲存
#歐拉法的算法，算法返回t,x
def countall(self):
for i in range(int(self.n)):
y_dere = -20*self.list[i]
#歐拉法疊加量y_dere = -20 * x
y_dere2 = -20*self.list2[i] + 0.5*400*self.h*self.list2[i]
#改進歐拉法疊加量 y_dere2 = -20*x(k) + 0.5*400*delta_t*x(k)
y_dere3 = (1-10*self.h)*self.list3[i]/(1+10*self.h)
#隱式梯形法計算 y_dere3 = (1-10*delta_t)*x(k)/(1+10*delta_t)
self.y += self.h*y_dere
self.y1 += self.h*y_dere2
self.y2 =y_dere3
self.list.append(float("%.10f" %self.y))
self.list2.append(float("%.10f"%self.y1))
self.list3.append(float("%.10f"%self.y2))
return np.linspace(0,1,int(self.n+1)), self.list,self.list2,self.list3
step = input("請輸入你需要求解的步長:")
step = float(step)
work1 = Euler(step,1)
ax1,ay1,ay2,ay3 = work1.countall()
#畫圖工具plt
plt.figure(1)
plt.subplot(1,3,1)
plt.plot(ax1,ay1,'s-.',MarkerFaceColor = 'g')
plt.xlabel('橫坐標t',fontproperties = 'simHei',fontsize =20)
plt.ylabel('縱坐標x',fontproperties = 'simHei',fontsize =20)
plt.title('歐拉法求解微分線性方程步長為'+str(step),fontproperties = 'simHei',fontsize =20)
plt.subplot(1,3,2)
plt.plot(ax1,ay2,'s-.',MarkerFaceColor = 'r')
plt.xlabel('橫坐標t',fontproperties = 'simHei',fontsize =20)
plt.ylabel('縱坐標x',fontproperties = 'simHei',fontsize =20)
plt.title('改進歐拉法求解微分線性方程步長為'+str(step),fontproperties = 'simHei',fontsize =20)
plt.subplot(1,3,3)
plt.plot(ax1,ay3,'s-.',MarkerFaceColor = 'b')
plt.xlabel('橫坐標t',fontproperties = 'simHei',fontsize =20)
plt.ylabel('縱坐標x',fontproperties = 'simHei',fontsize =20)
plt.title('隱式梯形法求解微分線性方程步長為'+str(step),fontproperties = 'simHei',fontsize =20)
plt.figure(2)
plt.plot(ax1,ay1,ax1,ay2,ax1,ay3,'s-.',MarkerSize = 3)
plt.xlabel('橫坐標t',fontproperties = 'simHei',fontsize =20)
plt.ylabel('縱坐標x',fontproperties = 'simHei',fontsize =20)
plt.title('三合一圖像步長為'+str(step),fontproperties = 'simHei',fontsize =20)
ax = plt.gca()
ax.legend(('$Eular$','$fixed Eular$','$trapezoid$'),loc = 'lower right',title = 'legend')
plt.show()
os.system("pause")
import numpy as np
import matplotlib.pyplot as plt
L = 0.01 #電容的值 F
C = 0.01 #電感的值 L
u_0 = 5 #電容的初始電壓
u_dot_0 = 0
def equition(u,u_dot):#二階方程
u_double_dot = -u/(L*C)
return u_double_dot
def draw_plot(time_step,time_scale):#時間步長和范圍
u = u_0
u_dot = u_dot_0 #初始電壓和電壓的一階導數
time_list = [0] #時間lis
Votage = [u] #電壓list
plt.figure()
for time in np.arange(0,time_scale,time_step):#使用歐拉數值計算法 一階近似
u_double_dot = equition(u,u_dot) #二階導數
u_dot = u_dot + u_double_dot*time_step #一階導數
u = u + u_dot*time_step #電壓
time_list.append(time) #結果添加
Votage.append(u) #結果添加
print(u)
plt.plot(time_list,Votage,"b--",linewidth=1) #畫圖
plt.show()
plt.savefig("easyplot.png")
if __name__ == '__main__':
draw_plot(0.0001,1)
import numpy as np
import matplotlib.pyplot as plt
L = 0.01 #電容的值 F
C = 0.01 #電感的值 L
R = 0.1 #電阻值
u_0 = 5 #電容的初始電壓
u_dot_0 = 0
def equition(u,u_dot):#二階方程
u_double_dot =(-R*C*u_dot -u)/(L*C)
return u_double_dot
def draw_plot(time_step,time_scale):#時間步長和范圍
u = u_0
u_dot = u_dot_0 #初始電壓和電壓的一階導數
time_list = [0] #時間lis
Votage = [u] #電壓list
plt.figure()
for time in np.arange(0,time_scale,time_step):#使用歐拉數值計算法 一階近似
u_double_dot = equition(u,u_dot) #二階導數
u_dot = u_dot + u_double_dot*time_step #一階導數
u = u + u_dot*time_step #電壓
time_list.append(time) #結果添加
Votage.append(u) #結果添加
print(u)
plt.plot(time_list,Votage,"b-",linewidth=1) #畫圖
plt.show()
plt.savefig("result.png")
if __name__ == '__main__':
draw_plot(0.0001,1)
