## Coupled nonlinear equations

Posted September 02, 2013 at 03:21 PM | categories: nonlinear algebra | tags:

Suppose we seek the solution to this set of equations:

\begin{align} y &=& x^2 \\ y &=& 8 - x^2 \end{align}To solve this we need to setup a function that is equal to zero at the solution. We have two equations, so our function must return two values. There are two variables, so the argument to our function will be an array of values.

from scipy.optimize import fsolve def objective(X): x, y = X # unpack the array in the argument z1 = y - x**2 # first equation z2 = y - 8 + x**2 # second equation return [z1, z2] # list of zeros x0, y0 = 1, 1 # initial guesses guess = [x0, y0] sol = fsolve(objective, guess) print sol # of course there may be more than one solution x0, y0 = -1, -1 # initial guesses guess = [x0, y0] sol = fsolve(objective, guess) print sol

[ 2. 4.] [-2. 4.]

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