How can I solve the fsolve function inside an ode15s function?

Hi,

I need to solve an fsolve function inside an ode15s function. However, the dependent variable in the differential equation is contained in the system of linear equations. How can I solve this? This is what I have but it says there is a problem:

 %file1.m 
clc; clear all; close all; format compact;
global A_T Fao P_tot DELTAHr E A R To Tf 
%Datos 
A_T = pi*1^2;%m
Fao = (66000*1000)/92.14; %kmol/año
P_tot = 50; %bar
DELTAHr = 49974; %KJ/Kmol
%Cálculo de k
E = 148114; 
A = 5.73E6;
R = 8.3144;
To = 600+273;
Tf = 635+273;
Zo = 0; 
Zf = 100;
yo = [To, 0];
[F fval flag] = fsolve('fun',[3 10])
[T, xa] =  ode15s('odefun', [Zo Zf], yo)
%file2.m
function F = fun(var)
global A_T Fao P_tot DELTAHr E A R To Tf FA FR CPA CPB CPR CPS CQP 
FB = var(1) 
FS = var(2)
Q = var(3)
F(1) =-FB + Fao*(5-x_a) + 0.9*Q ;
F(2) =-FS + Fao*(5/9 + x_a) + 0.1*Q;
F(3) = -Q +(FA*CPA*(T-To)+ FB*CPB*(T-To)+ FR*CPR*(T-To)+ FS*CPS*(T-To))/(CQP*(To-298)); 
end
%file3.m
function dvdz = odefun(T, x_a) 
global A_T Fao P_tot DELTAHr E A R To CPA CPB CPR CPS CQP FA FR
K = A*exp(-E/R*T);
CPA = 0.29  + 47.052E3*T - 15.716E6*T^2;
CPB = 3.249 + 0.422E3*T + 0.083E-5*T^-2;
CPR = -.206 + 39.064E3*T - 13.301E6*T^2;
CPS = 1.702 + 9.081E3*T - 2.164E6*T^2;
CQP = CPB*0.9 + CPS*0.1;
FA = Fao*(1-x_a);
FR = Fao*x_a;
var0 = [100 100 100];
[var] = fsolve('fun', var0);
var(1) = FB ;
var(2) = FS ;
var(3) = Q;
dvdz(1) = (A_T/Fao)*K*(P_tot/R*T)^1.5*(Fao*(1-x_a))*(((Fao*(5-x_a) + 0.9*Q))^0.5/(6.55*Fao + Q)^1.5);
dvdz(2) = (Fao*DELTAHr/(FA*CPA*(T-To)+ FB*CPB*(T-To)+ FR*CPR*(T-To)+ FS*CPS*(T-To)))*dvdz(1);
dvdz = dvdz'
end

Thank you!

[Torsten]

From your code above, I don't understand which system you are trying to solve.

If it helps: Usually, there is no Need to solve algebraic equations separately. The ODE solvers are suited to solve a mixture of algebraic and differential equations. Take a look at the differential-algebraic example under

http://radio.feld.cvut.cz/matlab/techdoc/math_anal/ch_8_od8.html

Best wishes

Torsten.