How to solve nonlinear system of equations

Hi,

I am trying to solve a flow network of various "nodes" or "stations" that have nonlinear relationships between them.

The non-linear relationships between them are created using regression (regress(y,X)) based on CFD data.

An example of one such relation would be:

P6 = P3 - (s36C + s36W*w + s36WW*w*w + s36N*N1 + s36NN*N1*N1);

where P6 is pressure at station 6, P3 is pressure at station 3, and s36C, s36W,s36N,s36NN refer to the constants from the regression, w is flow rate, N1 is speed, N1*N1 is speed squared).

I have relationships like this throughout my flow network from beginning to end.

I am currently solving it using an iterative approach where i guess an initial flow rate, and then solve the equations in nested loops to try to achieve convergence, but it is slow and likely not efficient.

I am looking for an appropriate solver within MATLAB that may handle this type of problem.

Any help would be greatly appreciated

Thank you.

[Torsten]

Maybe you could exchange your experiences:

https://de.mathworks.com/matlabcentral/answers/1676644-why-do-i-get-no-solution-found-in-fsolve-while-there-is-the-actual-value-for-them?s_tid=srchtitle

[Tyler]

Exactly what i needed, thank you!