# Solving PDEs using fsolve

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patilak on 18 Jul 2016
Answered: Torsten on 19 Jul 2016
I am trying to solve continuity, Navier-Stokes and heat transfer equation in 2-D cylindrical coordinates. I have discretized these equations. So now I have 4 non linear equations with 4 variables(u,v,T,f) such that: f1(u,v)=0 f2(u,v,f)=0 f3(u,v,f)=0 f4(u,v,f,T)=0
u-Axial velocity v-Radial velocity T-temperature f-liquid fraction (my problem involves solidification of metal)
Can I solve these using fsolve?

Alan Weiss on 18 Jul 2016
I do not understand how you propose to parameterize your problem so that fsolve would be appropriate. Don't you need to put a PDE solver in the solution process somehow?
Alan Weiss
MATLAB mathematical toolbox documentation

patilak on 18 Jul 2016
For two-dimensional PDE, PDE solver would only be the PDE toolbox?

Torsten on 19 Jul 2016
If your problem is stationary and you discretized your equations and boundary conditions correctly, this results in a big nonlinear system of equations for the solution variables in each grid point. So yes: fsolve can be used for solution if the size of your system is moderate.
Best wishes
Torsten.