How to solve nonlinear system of equations

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Tyler on 30 Mar 2022
Commented: Tyler on 30 Mar 2022
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.

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