基本原理
例题
代码
#四阶龙格-库塔法#求一阶常微分方程，相应的特解#x变量的区间a = 0b = 1#已知条件X = [0]Y = [1]h = 0.2 #设置步长n = (b-a)/h #步数def f(x,y):df = y-2*x/yreturn df#程序运行for i in range(int(n)):x1 = X[i]+hX.append(x1) #x1=x0+hk1 = f(X[i], Y[i])k2 = f(X[i]+h/2, Y[i]+h/2*k1)k3 = f(X[i]+h/2, Y[i]+h/2*k2)k4 = f(X[i]+h, Y[i]+h*k3)y1 = Y[i] + h/6*(k1+2*k2+2*k3+k4)Y.append(y1)list = []for i in range(len(X)):list.append([X[i],Y[i]])import pandas as pddataframe = pd.DataFrame(list)print(dataframe)
结果：
0 10 0.0 1.0000001 0.2 1.1832292 0.4 1.3416673 0.6 1.4832814 0.8 1.6125145 1.0 1.732142
