Thank you nh3simman

There are a lot to learn, I will try them.

I don't know the Broyden method, what's the advantage of it? I have searched and need to understand for detail. The Newton-Raphson method in a small loop sometimes goes wrong, cause exception or dead loop, so I wrote program use a gradual average method, usually steady but converged slowly.

I borrowed a book about optimization, seems no good method suitable for non-linear system, do you have suggestions?