i am busy by solving a non linear system of equations by using the Newton Raphson algorithm.

The problem is: during iterations: when we approach the solution it diverge( probably du to the derivative matrix equal zero), would you please help me solving this hadicap.

Sincerely

Make sure your matrix is well-posed(eigenvalues not too far off). If not, pre-condition it. Get the correct Jacobian matrices (the derivative matrix). For the final step, Add so-called Marquartz constants to diagonal to "stablize or make the matrix better-posed" the matrix, then iterate the Marquartz solutions, but eventually you got to remove the constant (gradually) to get the real solutions. I don't know that will help you.