MATLAB: Fsolve for17 simultaneous equations

arraycell arraysequationsfsolveOptimization Toolboxsimultaneousvariablevector

Hello,
I am attempting to set up an optimization code for solving a fluid dynamics problem. Since there are many unique variables, I wanted to know if there was a way to define each variable as part of a vector or array? I would like to be able to write my equations in terms of their native variables instead of x(0),x(1),x(2)…x(n).
Example: A = p(1), B = p(2), C = p(3)…., Q = p(17)
I realize that I there is likely a much better way, but this is the first problem of this magnitude that I have attempted. I have only used fsolve for single variable iterations prior to this and was unable to find an answer on this forum or Google. Likely due to the fact that I do not know the correct question to ask.
Thanks so much for the help.
 %function [F] = Fluids_Project_2a
format long;
options = optimset('TolFun', 1e-4, 'TolX', 1e-4, 'MAxIter',1e5,'MaxFunEvals',1e5);
%Variables
p{1}=Re1;
p{2}=Re2;
p{3}=Re3;
p{4}=u1;
p{5}=u2;
p{6}=u3;
p{7}=fF1; 
p{8}=fF2; 
p{9}=fF3; 
p{10}=F1; 
p{11}=F2; 
p{12}=F3; 
p{13}=P1;
p{14}=P2;
p{15}=Q1;
p{16}=Q2;
p{17}=Q3;
 %%Equations
%Effective Length/Diameter
LD1 = L1/D1 + E_L1*Eb90 + Ga_L1*Gate+ Contraction2to1;
LD2 = L2/D2 + E_L2*Eb90 + Ga_L2*Gate + Gl_L2*Globe + Contraction2to1;
LD3 = L3/D3 + E_L3*Eb45 + Ga_L3*Gate + Gl_L3*Globe;
%





F = {@(p) (rho*p(4)*D1/mu - p(1));
(Q1*4/pi/D1^2 - u1); 
((-1.737*log(0.269*epsilon/D1 - 2.185/p(1)*log(0.269*epsilon/D1 + 14.5/p(1))))^-2 - fF1);
(2*fF1*u1^2*(LD1) - F1);
%
%Pipe 2
(rho*u2*D2/mu - p(2)); %Re2

(Q2*4/pi/D2^2 - u2); %u2
((-1.737*log(0.269*epsilon/D2 - 2.185/p(2)*log(0.269*epsilon/D2 + 14.5/p(2))))^-2 - fF2); %Re2
(2*fF2*u2^2*(LD2) - F2); %F2
%
%Pipe 3
(rho*u3*D3/mu - p(3)); %Re
(Q3*4/pi/D3^2 -u3); %u3
((-1.737*log(0.269*epsilon/D3 - 2.185/p(3)*log(0.269*epsilon/D3 + 14.5/p(3))))^-2 - fF3); %fF3
(2*fF3*u3^2*(LD3) - F3); %F3
%
%Energy Balance
((Z_L2 - Z_L1) + AA*(P2 - P1 - 10)/(rho*g) + BB*F1/g);  %Node 1 -> 2
(AA*(P3 - P2)/(rho*g) + BB*F2/g);  %Node 2 -> 3
((Z_L3 - Z_L2) + AA*(P4 - P2)/(rho*g) + BB*fF3*Q3^2*(LD3)/g/D3^4);  %Node 2 -> 4
(P1 - (a-b*Q1^2));
%
%Mass flow
(Q1 - Q2 - Q3)};
%
p0 = [10000 10000 10000 10 10 10 .001 .001 .001 200 200 200 20 20 50 50 50];
h = fsolve(f,p0,options);

Best Answer

Nothing prevents you from unpacking the p(i) within the objective function to separate variables:
 function fval=myEquations(p)
   A = p(1); B = p(2); C = p(3)....; Q = p(17);
   fval(1)=A+B^2-C+Q;
   fval(2)= D+B^3-F;
   etc...
 end
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