FSOLVE GIVES SAME VALUE

clc;clearvars;close all; format short g;format compact;
tfinal=30;
pars.D=0.00005611;
pars.x2f=20;
pars.Y=0.4;
pars.beta=0.000055;
pars.k1=0.04545;
pars.alpha=2.2;
pars.mumax=0.000133;
pars.km=1.2;
pars.x3max=50;

csol2=fsolve(@(c) chemofun(c,pars),[5 4.5 15]);

function f=chemofun(c,pars)
f=zeros(3);
x1=c(1);
x2=c(2);
x3=c(3);
mumax=pars.mumax;
x3max=pars.x3max;
km=pars.km;
k1=pars.k1;
mu=((mumax)*x2*(1-(x3/(x3max))))/(km+x2+(x2^2)*(k1));
D=pars.D;
x2f=pars.x2f;
Y=pars.Y;
A=pars.alpha;
B=pars.beta;
f(1)=(mu-(D));
f(2)=(D)*(x2f-x2)-(mu*x1)/(Y);
f(3)=(-1)*(D)*x3+((A)*mu+B)*x1;
end

[JYOTI PRAKASH BEHERA]

need convergence to, x1=5.99, x2=5.02 and x3=19.05

[Alan Stevens]

You are trying to solve for x1, x2 and x3, but they only appear in two equations. There can be an infinite number of solutions.

[JYOTI PRAKASH BEHERA]

Mu have x1

[Alan Stevens]

Actually, it seems to have x2 and x3; but you are right, three equations are involved. The results seem very sensitive to the initial guesses though.

Answer 1

[Matt J]

clc;clearvars;close all; format short g;format compact;
tfinal=30;
pars.D=0.00005611;
pars.x2f=20;
pars.Y=0.4;
pars.beta=0.000055;
pars.k1=0.04545;
pars.alpha=2.2;
pars.mumax=0.000133;
pars.km=1.2;
pars.x3max=50;

fun=@(c) chemofun(c,pars);
opts=optimoptions('fsolve','StepTolerance',1e-12,'FunctionTolerance',1e-12,'OptimalityTolerance',1e-12);
[csol2,fsol2]=fsolve(fun,[5 4.5 15],opts)

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.

csol2 = 1×3

5.9905 5.0238 19.051

fsol2 = 1×3

-8.9331e-12 1.1261e-10 -9.9097e-11

function f=chemofun(c,pars)
f=zeros(1,3); %<-------


x1=c(1);
x2=c(2);
x3=c(3);
mumax=pars.mumax;
x3max=pars.x3max;
km=pars.km;
k1=pars.k1;
mu=((mumax)*x2*(1-(x3/(x3max))))/(km+x2+(x2^2)*(k1));
D=pars.D;
x2f=pars.x2f;
Y=pars.Y;
A=pars.alpha;
B=pars.beta;
f(1)=(mu-(D));
f(2)=(D)*(x2f-x2)-(mu*x1)/(Y);
f(3)=(-1)*(D)*x3+((A)*mu+B)*x1;
end