Solving system of non-linear equations

Hi, I am new to this program. I am currently given one project, finding the steady state values of a wastewater treatment system using Activated Sludge Model (ASM model) which consist about 10 non-linear equations (means about 10 components) or more than that simultaneously.

For further explanation, by using mass balance equation:

Accumulation = mass in - mass out + reaction - consumption

At steady state, accumulation = 0

I am given the inlet component value, the reaction and consumption equation is represented by ASM model, and the steady value of the component at the outlet is same as ASM model (reaction and consumption). Example mass balance of component x1:

0=x1i-x1+(x3*x5/x1)+x1*(1-x4)-(x2*x3)

With more than 10 equations and I want to get the steady state of x1,x2,x3.... simultaneously

1. How to solve this with reference of MATLAB coding? (numerically like secant, newton method? using fsolve? or any other idea?)

2. How can we determine if there is more than one steady state value? (graphical method??)

[imen baklouti]

hi sir

please i need the equation of input qin (t) fresh water input flow thanks

Answer 1

[Torsten]

ad 1) Use fsolve.

ad 2) Use different initial guesses for x1, x2, ... .

Best wishes

Torsten.

[chinhui ooi]

thanks for answering my question any relevant reference about fsolve?

any other method to detect more than one steady state value? is it possible to use graphical method with relevant reference??

[Torsten]

thanks for answering my question any relevant reference about fsolve?

http://de.mathworks.com/help/optim/ug/fsolve.html

any other method to detect more than one steady state value? is it possible to use graphical method with relevant reference??

Graphical methods for a system with 5 unknowns ? No.

Best wishes

Torsten.