fsolve with two variables in a loop

Hi, I thank you in advance.

I try to solve two equation with two variables (x and y) with a changing parameters T, i try to use a fsolve method. I met a problem in the loop. Below is my code.

clear all
% effective normal stress (Pa)
p.sigma=5e7;p.To=273.15+20;p.R=8.314;p.K=6e10;p.Lt=8e-4;p.lambda=0.0625;
p.phio=0.32;p.dsb=2e-6;p.dbulk=2e-5;p.qsb=0.4;p.phic=0.2;p.phio=0.02;
p.qbulk=0.7;p.H=0.577;p.n=1.7;p.m=3;p.An=0.0759;p.At=4.4*p.An;
p.Ea=213e3;p.omega=3.69e-7;p.muo=0.6;p.ao=0.006;p.xo = 0.1813;
p.V0=1e-6;p.V1=0.1e-6;p.gammao=0.02;p.M = 2;p.N = 1;


% a changing parameter T with two variables x and y
T=linspace(273.15,600,100);
x=linspace(0,0.2,100);
y=linspace(0,0.2,100);

% Equation 1: At reference (prestep) velocity of V0
fx=@(x,T) p.Lt.*p.lambda./p.V0*p.An.*exp(-p.Ea./p.R./T).*...
    (p.sigma).^p.n./(p.dsb).^p.m.*((p.phic-x)./(x-p.phio)).^(-p.M)-p.H.*(p.qsb-2.*x).^p.N;
% Equation 2: At a velocity (poststep) of V1
fy=@(Y,T) p.Lt.*p.lambda./p.V1*p.An.*exp(-p.Ea./p.R./T).*...
    (p.sigma).^p.n./(p.dsb).^p.m.*((p.phic-y)./(y-p.phio)).^(-p.M)-p.H.*(p.qsb-2.*y).^p.N;

musi=@(T) p.muo+p.ao*T./p.To.*log(p.V1./p.V0);
muso=p.muo;
tanso=@(x) p.H.*(p.qsb-2.*x).^p.N;
tansi=@(y) p.H.*(p.qsb-2.*y).^p.N;
aa=@(x,T) p.ao.*T./p.To.*(1+tanso(x).^2)./(1-muso.*tanso(x))./(1-musi(T).*tanso(x));
bb=@(y,T) -tansi(y).*(1+musi(T).^2)./(1-musi(T).*tansi(y))./...
    (1-musi(T).*tansi(y)).*(1-(p.V1./p.V0).^(1/(p.M+p.N)))./log(p.V1./p.V0);

% loop
options=odeset('Refine',1,'RelTol',1e-15,'InitialStep',1e-6,'MaxStep',3e6);
for j=1:length(T)
  fun=@(x,y)[fx(x,T(j));fy(y,T(j))];
  z(:,j)=fsolve(fun,[0.199;0.199],options); %plotted to get initial guess close.
end

Not enough input arguments.

Error in solution (line 33)
fun=@(x,y)[fx(x,T(j));fy(y,T(j))];

Error in fsolve (line 264)
fuser = feval(funfcn{3},x,varargin{:});

Caused by:
Failure in initial objective function evaluation. FSOLVE cannot continue.

% figure
plot(T-273.15,aa(z,T),'k-',T-273.15,aa(z,T),'r-');

[Torsten]

If the solutions from the symbolic code did not satisfy your constraints, using "fsolve" won't help.

The three solutions you got for x and y from the symbolic approach are the only ones your equations have.

[Mei Cheng]

@Torsten thanks for your remind. Previously i used the fsolve to get a good result, but it is for one variable. I guess it should work for two variables.

Answer 1

[Matt J]

fun=@(z)[fx(z(1),T(j));fy(z(2),T(j))];

[Mei Cheng]

@Matt J thanks for your reply.

i run the code, then:

" Error using vertcat

Dimensions of arrays being concatenated are not consistent."

there is a problem:

z(:,j)=fsolve(fun,[0.199;0.199],options);

It is a format problem?

[Matt J]

You need to test your objective fun() before giving it to fsolve. It looks like fx is a scalar and fy is a row vector, so they can't be concatenated vertically.

[Mei Cheng]

@Matt J thanks for your reply. I guess i have fixed the problem. one last question for the plot.

For the plot, do I need to modify the below code. As the z(1) and z(2) works for different fx and fy, respctively.

aa uses z(1), bb uses z(2).

plot(T-273.15,aa(z,T),'k-',T-273.15,bb(z,T),'r-');

% or like below code
plot(T-273.15,aa(z(1),T),'k-',T-273.15,bb(z(2),T),'r-');

% like below code
plot(T-273.15,aa(z(:,1),T),'k-',T-273.15,bb(z(:,2),T),'r-');

% actually, i have checked them, they are not working.

[Matt J]

Since z(:,i) are column vectors, perhaps T should be a column-vector as well?

plot(T-273.15,aa(z(:,1),T(:)),'k-',T-273.15,bb(z(:,2),T(:)),'r-');

[Mei Cheng]

@Matt J thank you very much for your suggestions. I have reivsed my code accordingly.