Solve 4 equations with 3 unknowns

Hi, I have the 4 equations mentioned below. I Ca,Cb,Cc are unknown. For a user input of Cd, I want to solve of the rest. The calculated numbers should ideally not be negative.

'Z' can be treated as different under inputs (they are not variables) Equations:

(Z-Z*Ca)/(Z) - Z*Ca*Cb=0
(Z-Z*Cb)/(Z) - (Z*Ca*Cb+Z*Cb*Cc) = 0
(-Z*Cc/Z)   + Z*Ca*Cb-Z*Cb*Cc  = 0
-Z*Cd/(Z) + Z*Cb*Cc = 0   (Cd is an input by the user too)

Need help with the matlab code

[Ameer Hamza]

Your system is Overdetermined, you will not get a solution unless one of the equations is linearly dependent on other equations (highly likely). Do you want a solution in the least square sense as done by @Torsten?

Answer 1

[Torsten]

Cd=...;
Z=...;
fun=@(x)[1-x(1)-Z*x(1)*x(2);1-x(2)-Z*x(2)*(x(1)+x(3));-x(3)+Z*x(2)*(x(1)-x(3));-Cd+Z*x(2)*x(3)];
lb=[0 0 0];
ub=[Inf Inf Inf];
x0=[1 1 1];
x = lsqnonlin(fun,x0,lb,ub);
Ca = x(1)
Cb = x(2)
Cc = x(3)

Best wishes

Torsten.

[Torsten]

I just listed your four equations here where I set Ca=x(1), Cb=x(2) and Cc=x(3).

E.g.

(Z-Z*Ca)/(Z) - Z*Ca*Cb=0
-> 1-Ca-Z*Ca*Cb=0
-> 1-x(1)-Z*x(1)*x(2)=0

It should be easy for you to alter the line if the Z's are different.

Best wishes

Torsten.

[Remston Martis]

yes i read it wrong.. works perfectly. Thanks!