Non linear solver

1

I am trying to solve a system of 8 non linear equations using Newton-Raphson method. But It does not seem to work. I have used LAPACK. But, no luck. Is there any better ways solve them?

2

Try looking for MINPACK hybrd1.f, and welcome.

3

C05QSF if you have access to NAG Library.

4

You could also consider: GitHub - jacobwilliams/nlesolver-fortran: Nonlinear Equation Solver with Modern Fortran

Disclaimer: I have not used it.

5

This can be a very difficult problem. I have had success using homotopy methods. Many years ago I used HOMPACK90. We then rolled our own simplified version optimized for our problem.

The basic idea is you have a set of non-linear equations G(x)=0. You parameterize the system with a (perhaps artificial) parameter λ to give G(x,λ)=0, where G(x,λ)=0 is easier to solve when λ=0. You solve the equation for the initial loading λ=0 then use previous solutions as the starting point as you increment λ to the final value.

See: