How to solve this complicated non-linear function?

Question

The code is giving the same output as my guess value in fsolve function

import numpy as np
import math
from scipy.optimize import fsolve
def f(y):

    a11 = 17.20
    iv_y = np.sqrt(pi)*np.sqrt(y)*np.exp(y)*math.erfc(np.sqrt(y))
    b11 = 86.02
    dr = 1-(0.92*iv_y)
    g = -(y*a11)/dr - (b11*iv_y)/dr - 50
    return g
pe = fsolve(f,10)
print(pe)

Any reason why it is giving the same output as my guess value 10?

Answer 1

The fsolve function is printing the warning: "RuntimeWarning: The iteration is not making good progress, as measured by the improvement from the last ten iterations." This means that fsolve cannot find a solution.

We can see why it cannot find a solution if we look at a plot of your function"

You can see that the function is negative and monotonically decreasing. It is not defined for negative arguments. So essentially, you are asking fsolve to find a solution that doesn't exist; the function despairs at this hopeless task and just returns the original guess.