python 解决微分方程的操作(数值解法)

```python
```python
import numpy as np
from scipy.integrate import odeint
from matplotlib import pyplot as plt
import os
#先从odeint函数直接求解微分方程
#创建欧拉法的类
class Euler:
    #构造方法，当创建对象的时候，自动执行的函数
    def __init__(self,h,y0):
        #将对象与对象的属性绑在一起
        self.h = h
        self.y0 = y0
        self.y = y0
        self.n = 1/self.h
        self.x = 0
        self.list = [1]
        #欧拉法用list列表,其x用y叠加储存
        self.list2 = [1]
        self.y1 = y0
        #改进欧拉法用list2列表，其x用y1叠加储存
        self.list3 = [1]
        self.y2 = y0
        #隐式梯形法用list3列表，其x用y2叠加储存
    #欧拉法的算法，算法返回t,x
    def countall(self):
        for i in range(int(self.n)):
            y_dere = -20*self.list[i]
            #欧拉法叠加量y_dere = -20 * x
            y_dere2 = -20*self.list2[i] + 0.5*400*self.h*self.list2[i]
            #改进欧拉法叠加量 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)
            #隐式梯形法计算 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("请输入你需要求解的步长:")
step = float(step)
work1 = Euler(step,1)
ax1,ay1,ay2,ay3 = work1.countall()
#画图工具plt
plt.figure(1)
plt.subplot(1,3,1)
plt.plot(ax1,ay1,'s-.',MarkerFaceColor = 'g')
plt.xlabel('横坐标t',fontproperties = 'simHei',fontsize =20)
plt.ylabel('纵坐标x',fontproperties = 'simHei',fontsize =20)
plt.title('欧拉法求解微分线性方程步长为'+str(step),fontproperties = 'simHei',fontsize =20)
plt.subplot(1,3,2)
plt.plot(ax1,ay2,'s-.',MarkerFaceColor = 'r')
plt.xlabel('横坐标t',fontproperties = 'simHei',fontsize =20)
plt.ylabel('纵坐标x',fontproperties = 'simHei',fontsize =20)
plt.title('改进欧拉法求解微分线性方程步长为'+str(step),fontproperties = 'simHei',fontsize =20)
plt.subplot(1,3,3)
plt.plot(ax1,ay3,'s-.',MarkerFaceColor = 'b')
plt.xlabel('横坐标t',fontproperties = 'simHei',fontsize =20)
plt.ylabel('纵坐标x',fontproperties = 'simHei',fontsize =20)
plt.title('隐式梯形法求解微分线性方程步长为'+str(step),fontproperties = 'simHei',fontsize =20)
plt.figure(2)
plt.plot(ax1,ay1,ax1,ay2,ax1,ay3,'s-.',MarkerSize = 3)
plt.xlabel('横坐标t',fontproperties = 'simHei',fontsize =20)
plt.ylabel('纵坐标x',fontproperties = 'simHei',fontsize =20)
plt.title('三合一图像步长为'+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")

pip install numpy 
pip install matplotlib

import numpy as np
import matplotlib.pyplot as plt
 
L = 0.01  #电容的值 F
C = 0.01  #电感的值 L
u_0 = 5   #电容的初始电压
u_dot_0 = 0
 
def equition(u,u_dot):#二阶方程
    u_double_dot = -u/(L*C)
    return u_double_dot
 
def draw_plot(time_step,time_scale):#时间步长和范围
    u = u_0
    u_dot = u_dot_0  #初始电压和电压的一阶导数
    time_list = [0] #时间lis
    Votage = [u] #电压list
    plt.figure()
    for time in np.arange(0,time_scale,time_step):#使用欧拉数值计算法 一阶近似
        u_double_dot = equition(u,u_dot) #二阶导数
        u_dot = u_dot + u_double_dot*time_step #一阶导数
        u = u + u_dot*time_step #电压
        time_list.append(time) #结果添加
        Votage.append(u) #结果添加
        print(u)
    plt.plot(time_list,Votage,"b--",linewidth=1) #画图
    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  #电容的值 F
C = 0.01  #电感的值 L
R = 0.1   #电阻值
u_0 = 5   #电容的初始电压
u_dot_0 = 0
 
def equition(u,u_dot):#二阶方程
    u_double_dot =(-R*C*u_dot -u)/(L*C)
    return u_double_dot
 
def draw_plot(time_step,time_scale):#时间步长和范围
    u = u_0
    u_dot = u_dot_0  #初始电压和电压的一阶导数
    time_list = [0] #时间lis
    Votage = [u] #电压list
    plt.figure()
    for time in np.arange(0,time_scale,time_step):#使用欧拉数值计算法 一阶近似
        u_double_dot = equition(u,u_dot) #二阶导数
        u_dot = u_dot + u_double_dot*time_step #一阶导数
        u = u + u_dot*time_step #电压
        time_list.append(time) #结果添加
        Votage.append(u) #结果添加
        print(u)
    plt.plot(time_list,Votage,"b-",linewidth=1) #画图
    plt.show()
    plt.savefig("result.png")
 
if __name__ == '__main__':
    draw_plot(0.0001,1)