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

Question

Yavar Hayat 2019-4-9

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/455232-plotting-the-solution-of-multi-variable-non-linear-equations-solved-using-fsolve

评论： Yavar Hayat 2019-4-10

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?

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Stephan 2019-4-9

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 2019-4-9

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

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Answer 1

Torsten 2019-4-9

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/455232-plotting-the-solution-of-multi-variable-non-linear-equations-solved-using-fsolve#answer_369743

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

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Walter Roberson 2019-4-10

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 2019-4-10