How do I solve a non-linear linked system of equations
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so I need to solve for chemical equilibrium of several product species in the combustion of CH4 and O2, so I am solving for the following unknowns [n_CO2,n_H2O,n_CO,n_OH,n_O2,n_H2,n_O,n_H] using the following equations
hydrogen balance 0=.5n_H2O+n_OH+.5n_H2+n_H-4
carbon balance 0=n_CO2+n_CO-1
Oxygen balance 0=.5n_CO2+n_H2O+n_CO+n_OH+.5n_O2+n_O
all of the previous equations were obviously linear, but now we get to the linked non-linear equations, in the following equations P is a known pressure, k_pn are constants that are also already known, and n is the sum of all the unknowns
CO+O<->CO2
0=n_CO2/(n_CO*n_O)-(P/n)*k_p1
OH+H<->H2O
0=n_H2O/(n_OH*n_H)-(P/n)*k_p2
2O<->O2
0=n_O2/(n_O^2)-(P/n)*k_p3
2H<->H2
0=n_H2/(n_H^2)-(P/n)*k_p4
O+H<->OH
0=n_OH/(n_O*n_H)-(P/n)*k_p5
I know the upper and lower limits of each unknown, so additionally, how would I specify those in whatever solver I would end up using?
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