解联立方程组 xp^2=40-x=(13-x)q^2 ，p-1-q=0 ，求 x,p,q

wintex

請問聯立方程式

Nicolas2050

这类简单非线性方程组都有成熟的算法。

Nicolas2050

#非线性方程组
from gekko import GEKKO
m = GEKKO()             # create GEKKO model
x = m.Var(value=2)      # define new variable, initial value=0
p = m.Var(value=1)      # define new variable, initial value=1
q = m.Var(value=1)      # define new variable, initial value=1
m.Equations([p-1-q==0, 40-x==(13-x)*q**2,x*p**2==40-x])  # equations
m.solve(disp=False)     # solve
print([x.value[0],p.value[0],q.value[0]]) # print solution
结果：
[3.9999999831, 3.0000000017, 2.0000000017]

Nicolas2050

#非线性方程组
from gekko import GEKKO
m = GEKKO()             # create GEKKO model
x = m.Var(value=2)      # define new variable, initial value=0
p = m.Var(value=1)      # define new variable, initial value=1
q = m.Var(value=1)      # define new variable, initial value=1
m.Equations([p-1-q==0, 40-x==(13-x)*q**2,x*p**2==40-x])  # equations
m.solve(disp=False)     # solve
print([x.value[0],p.value[0],q.value[0]]) # print solution
结果：
[3.9999999831, 3.0000000017, 2.0000000017]

Nicolas2050

# -*- coding: utf-8 -*-
"""
Created on Sun Feb 23 14:03:29 2020
One is mever too old to learn.
@author: NicholasTU
Nonlinear Equations
p-1-q==0, 40-x==(13-x)*q**2,x*p**2==40-x
"""

import numpy as np
from scipy.optimize import fsolve

def myFunction(z):
   x = z[0]
   p = z[1]
   q = z[2]

   F = np.empty((3))
   F[0] =p-1-q
   F[1] =40-x-(13-x)*q**2
   F[2] = x*p**2-40+x
   return F

zGuess = np.array([4,3,2])
z = fsolve(myFunction,zGuess)
print(z)
[4. 3. 2.]

luyuanhong