Plotting the solution of multi-variable non-linear equations (solved using fsolve).

These are the equations:

function [fval]= ptfunc(X)
Tcell=X(1);
Pcell=X(2);
Qh=X(3);
Pteg=X(4);
alpha = 0.95;
A = (0.04)^2; 
epsilon = 0.88; 
sigma = 5.69*10^(-8); 
Ta = 298.15; 
u=(0.003+1/5)^-(1);
ns = 0.10; 
theta = 0.0011; 
An=6.4*10^-7;
Hn=0.01;%:0.01:0.06;
N=62;
S=185*10^-6;
rho=10^-5;
den=2*rho;
k=1.5;
Z=(S^2)/(rho.*k);
Tc=298;
r=0.2;
n=0.0001;
hc=0.00009;
num2=2*r*hc;
G=500;
fval(1,1)= -Qh+ alpha*G*A-u*A*(Tcell-Ta)-epsilon*sigma*A*((Tcell.^4)-(Ta^4))-Pcell;
fval(2,1)= -Pcell+ alpha*G*A*ns.*(1-theta.*(Tcell - 298));
fval(3,1)= -Qh + (k*An*N/Hn)*(1-Z*(3*Tcell+Tc)/8)*(Tcell-Tc);
fval(4,1)= -Pteg+(S^2)*An*N*((Tcell-Tc)^2)./(den.*(n+Hn).*(1+num2./Hn).^2);

I need to plot the varaibles with respect to G. How do I do that?

[Stephan]

G is a scalar - its value is 500 - so you would plot 4 single points - one for each result from fsolve. Is this what you want to do?

[Yavar Hayat]

No. I want to the values of G so as to plot the four variables accordglingly.

Answer 1

[Torsten]

function main
  G = linspace(250,750).';
  X0 = [1,1,1,1];
  for i=1:numel(G)
    sol = fsolve(@(X)ptfunc(X,G(i)),X0);
    x(i,:) = sol;
    X0 = sol;
  end  
  plot(G,x(:,1))
end

function fval = ptfunc(X,G)
  Tcell=X(1);
  Pcell=X(2);
  Qh=X(3);
  Pteg=X(4);
  alpha = 0.95;
  A = (0.04)^2; 
  epsilon = 0.88; 
  sigma = 5.69*10^(-8); 
  Ta = 298.15; 
  u=(0.003+1/5)^-(1);
  ns = 0.10; 
  theta = 0.0011; 
  An=6.4*10^-7;
  Hn=0.01;%:0.01:0.06;
  N=62;
  S=185*10^-6;
  rho=10^-5;
  den=2*rho;
  k=1.5;
  Z=(S^2)/(rho.*k);
  Tc=298;
  r=0.2;
  n=0.0001;
  hc=0.00009;
  num2=2*r*hc;
  %G=500;
  fval(1,1)= -Qh+ alpha*G*A-u*A*(Tcell-Ta)-epsilon*sigma*A*((Tcell.^4)-(Ta^4))-Pcell;
  fval(2,1)= -Pcell+ alpha*G*A*ns.*(1-theta.*(Tcell - 298));
  fval(3,1)= -Qh + (k*An*N/Hn)*(1-Z*(3*Tcell+Tc)/8)*(Tcell-Tc);
  fval(4,1)= -Pteg+(S^2)*An*N*((Tcell-Tc)^2)./(den.*(n+Hn).*(1+num2./Hn).^2);
end

[Yavar Hayat]

I get one graph using your code. How do I get all four or choose one of them.

[Torsten]

plot(G,x)

instead of

plot(G,x(:,1))

[Walter Roberson]

However, it is working. The reason it does not look like it is working is that one of the results is on the order of 300, and two of them are on the order of 0.1, and the last of them is on the order of 0.01 . You simply cannot see anything in 3 of the 4 lines because they are insignificant on the scale of the first plot.

You could use subplot() to break the values out.

If you have a new enough MATLAB you could use stackedplot()

[Yavar Hayat]

I got it by using

plot(G,x(:,1))
plot(G,x(:,2))

etc.

Thank you.