The Newton-Raphson Method and What to do When It Fails

I've been working on a system which uses Newton-Raphson method to solve a system of equations which model the flow of fluids along a channel. We've had great results during initial testing but the system fails miserably in some occasions. This is a limitation which is inherently present in Newton-Raphson iterative method which makes the system diverge. The best solution would be to move to a different numerical scheme which guarantees global convergence.
The other method is to modify the scheme in such a way that convergence is guaranteed ( or the system converges for all valid system parameter values).
While searching for how to achieve this, I came across this page, which gives details of the Damped Newton-Raphson method, which mediates iteration values, hence forcing the system to converge. To use this method to achieve global convergence would take a lot of work and enforce a heavy toll on the processor. It's best to use this iff the normal iteration fails inside a time step.


It's the best option we have at the moment. I would post about the effectiveness of the method after implementing it in our model. 


Newton-Raphson method with example VB code