My question was whether or not successive over-relaxation (http://en.wikipedia.org/wiki/Successive_over-relaxation) could be used to find solutions to a nonlinear equation. In particular I am interested if it is possible to obtain multiple solutions (assuming your nonlinear ode has multiple solutions) by varying your choice of values for the first iteration.
Thanks
The short answer is yes. If your problem has been reduced to a system of non-linear algebraic equations, then, generally, that must be solved iteratively. There are many methods -- but the first step is to find local solutions by linearizing the system. The SOR can be used to solve the linear system.
If the solution is not unique - then which solution is obtained (if any) depends more on the initial guess - and probably not the relaxation parameter which may control rate of convergence.
For a simple analogy consider how Newton's method is used to find the roots of a single non-linear equation.