自学教程：python 解决微分方程的操作(数值解法)

```python```pythonimport numpy as npfrom scipy.integrate import odeintfrom matplotlib import pyplot as pltimport 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.list3step = 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pltplt.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 npimport matplotlib.pyplot as plt L = 0.01  #电容的值 FC = 0.01  #电感的值 Lu_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 npimport matplotlib.pyplot as plt L = 0.01  #电容的值 FC = 0.01  #电感的值 LR = 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)