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The type of nonlinear system need be clarified. Is it system of scalar nonlinear equations? system of nonlinear BVPs of ODEs or PDEs? System of nonlinear IBVPs of ODEs or PDEs...?
In case of the usual system of nonlinear scalar equations, the matlab symbolic tool (command) ''solve or fsolve'' may be used. Numerical methods are Newton method, Halley's method, Chebyshev's method....There are references with matlab codes using the iteration methods, and also written codes are available for systems of nonlinear BVPs or IBVPs. There can be different ways to solve....