4階(經典)龍格-庫塔法解微分方程組-基於Python
我真是服了，CSDN找不到Python實現的麼？？非得我來寫？？？
後續會把一些講解補上，因爲要考試了。。。，直接上例題
'''
@Author: ChangWenhan
@Date: 2020-05-04 01:34:36
@LastEditTime: 2020-05-04 01:07:20
@Description: mdzz
'''
import numpy as np
import math as m
from sympy import *
import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif']=['SimHei'] #顯示中文標籤
plt.rcParams['axes.unicode_minus']=False
xarray=[]
yarray=[]
array=[]
def f(x,y):
a=x+2*y
return a
def g(x,y):
a=3*x+2*y
return a
def RK4():
h=0.02
a=0
x=6
y=4
while a<=0.2:
array.append(a)
xarray.append(x)
yarray.append(y)
a+=h
f1=f(x,y) #第一步
m1=x+f1*h/2
g1=g(x,y)
n1=y+g1*h/2
f2=f(m1,n1) #第二步
m2=x+f2*h/2
g2=g(m1,n1)
n2=y+g2*h/2
f3=f(m2,n2) #第三步
m3=x+f3*h
g3=g(m2,n2)
n3=y+g3*h
f4=f(m3,n3) #第四步
g4=g(m3,n3)
x=x+(f1+2*f2+2*f3+f4)*h/6
y=y+(g1+2*g2+2*g3+g4)*h/6
def main():
RK4()
for i in xarray:
print(i)
print("-------------")
for i in yarray:
print(i)
plt.figure(12)
plt.subplot(212)
plt.scatter(xarray, yarray, alpha=0.6)
plt.subplot(221)
plt.scatter(array, xarray, alpha=0.6)
plt.subplot(222)
plt.scatter(array, yarray, alpha=0.6)
plt.show()
if __name__ == "__main__":
main()
