I have a system of two nonlinear equations (f(x,y)=0 and g(x,y)=0) to which I want to find all roots over a region (say x from -5 to 5 and y from -5 to 5).
The problem with using fsolve is that I need to supply the initial guesses which may not be known easily. If the region where I am looking for solutions is small, I guess I could take a lot of initial guesses and get the solutions. However, I want to know if a more robust method exists.
One approach is tried was to find the values of (x,y) where f(x,y) and g(x,y) simultaneously change their sign and feeding those as the initial conditions. This approach works reasonably well until you supply equations which don't change sign after a zero crossing. (For example f(x,y) = x^2)
Any help/suggestion is appreciated!
Thanks,
Mohit
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