fsolve Python函数，增加错误

Question

I am trying to solve a four nonlinear equation system using the scipy.optimize function fsolve .

def equations(p):
   e1, e2, F, B = p

   Eq_F1 = (-F + Fa(4, e1, e2) + Fa(5,e1, e2) - A1*Acc1(e1, e2))
   Eq_T1 = (F*L + Fa(4,e1, e2)*A2 + Fa(5, e1, e2)*A3
   Eq_F2 = (Fb(1, e1, B)*A4*math.cos(B) + Fb(2,e1)*A5 + Fb(3,e1)*A6 + F*np.cos(alpha(e1, e2))- A7*Acc2)
   Eq_T2 = (Fb(1,e1, B)*math.cos(B)*A8- F*np.cos(alpha(e1, e2))*A9- Fb(2,e1)*A10- Fb(3,e1)*A11

   return (Eq_F1, Eq_T1, Eq_F2, Eq_T2)

Where Fa , Fb et alpha are functions of e1 , e2 and of a number. Ai are constants I introduced to give you a global vision of the system. I solve the system as following:

e1, e2, F, B  = fsolve(equations,(0.3,5,100,0.1), xtol=1.49012e-14)

Where the first guessing is reasonable knowing my problem.

The results given being false, I introduced print(e1, e2, F, B) in the equations function. What a surprise ! If the first values are 0.3, 5, 100, 0.1 , they immediately jump to extreme values on the second one, impeding the convergence... Thus the results turn far from relevant.

Has anyone got an idea ?

Answer 1

I can't reproduce your code because I don't have all the constants. Without knowing the exact details of your problem, I cannot be sure, but I will guess there is a high probability of a numerical issue here .

fsolve is a function that implements an algorithm in numerical analysis , and it iterates towards an approximate solution. Numerical algorithms can be "touchy" in the sense that if the user does not use the right settings for a particular problem, or if the particular choice of algorithm is unsuited for the problem, errors can result.

• Your starting point might be bad -- numerical algorithms can be very sensitive to the choice of starting point.
• Your xtol might be way too small -- this can lead to tiny step sizes in the iteration of the algorithm which prevents convergence and also causes numerical error (eg rounding error) to accumulate.