I want to solve a system of nonlinear equations like
where m is an external parameter on which the equations depends on.
As the equations are very hard, what I do is to explicitly fix m, above all, and then find a solution for that specific value of m (by FindRoot). But this is very slow and inefficient (and more specifically in my case, where indeed I have three parameters).
What I would like is an automatic method that studies numerically the solution for a discrete set of values for m, that fixes it without that I explicitly change it from time to time. So that I would get all together the solutions for those values of m.
It would be nice also that a similar procedure can be applied to the initial seeds for FindRoot , since in my case I get several solutions changing the latter, and so there are different solutions for that value of m, and so similarly I would like to have all the solutions for a given set of initial seeds.
Is it possible to do such a thing? How?