Solve system of equations with 4 + 2N equations

Hello, I would like to implement on matlab different systems of equations, all connected to one another. I have a total of 4 + 2N equations (2 equations at the 2 edges of my geometry and 2N equations - the internal parts of my geometry).

Here is an example of the code (not working), just to give you an idea of what I mean:

%unknowns
Qm = zeros(Ntot,1);
T = zeros(Ntot,1);
Qc = 0; 
Qh = 0;

for ii=1:N 
    
    %system 1
    Qm(1) = -Qc + q0 - Pc - qw/2; 
    T(1) = T0 - Rc*Qc;
    
    %system i
    T(ii) - T(ii-1) = R1/Nc*q0 - R1/Nc*Qm1;
    T(ii) - Rg0/Nc*Qm(ii-1) + Rg0/Nc*Qm(ii) = T0;
    
    %system N
    Qh - Qm(N) = Ph - q0 + qw/2; 
    T(N) - T0 = Rh0*Qh;
    
end

How can I implement this on Matlab?

Answer 1

[Alan Stevens]

Not entirely clear to me what you want, but perhaps something like the following, where the edge equations are taken outside the loop:

% Arbitrary data
Qc = 0; 
Qh = 0;
q0 = 1000;
Pc = 1;
Ph = 1;
qw = 1;
Rc = 1;
R1 = 1;
Rg0 = 1;
Rh0 = 1;
Nc = 1;
T0 = 10;
Ntot = 10;

%unknowns
Qm = zeros(Ntot,1);
T = zeros(Ntot,1);

%system 1
Qm(1) = -Qc + q0 - Pc - qw/2; 
T(1) = T0 - Rc*Qc;


for ii=2:Ntot-1 

    %system i
    T(ii) = T(ii-1) + R1/Nc*q0 - R1/Nc*Qm(ii-1);
    Qm(ii) = Qm(ii-1) + (T0 - T(ii))*Nc/Rg0; 
    
end

%system N
Qm(Ntot) = Qh - (Ph - q0 + qw/2); 
T(Ntot) = T0 + Rh0*Qh;

plot(Qm,T),grid

[letoppina]

Thanks, it was very sueful. However, Qc and Qh are also unknown variables. How can I initiate them without giving them a fixed value?

[Alan Stevens]

You will need equations that describe them.