How can I find a correct value of the guess for my system of non linear equations ??

2 vues (au cours des 30 derniers jours)
kamal kiki
kamal kiki le 15 Fév 2012
I want to solve the following system of 3 non linear equations using fsolve.The unknowns to be found are X , Y and Z.
X-241.4*[(1.919*10^-8)*Y^1.429-(5.492*10^-10)*Y^1.714]^(1/2)=0
X*(3.121*10^5)+42.29-X*Z*1117-2.482*Z=0
X+0.002222-0.001976*Y*Z^(-1/2)=0
In order to solve this system using fsolve I have to enter a value of a guess for the values of X , Y and Z.
Please is there any way of finding a correct guess for this system ????
When I run fsolve with a random guess, I receive the message
Maximum number of function evaluations reached:
increase options.MaxFunEvals.

Réponses (2)

Walter Roberson
Walter Roberson le 15 Fév 2012
You can use the first equation to isolate X in terms of Y. Substitute that X in to the second equation and then you can isolate Z in terms of Y. Substitute the X and Z in to the third equation to get an expression for Y. You can then work on just that expression in one variable.
When the floating point coefficients are converted to rational form, the expression for Y contains as a repeated sub-expression sqrt(56414126863825657569157648*Y^(1429/1000)-1614519984922625768635418*Y^(857/500)) . You can solve() this for Y and take the larger of the two solutions (the smaller is 0) and use that as an initial guess for your fsolve(). The actual solution is reasonably close by.
  1 commentaire
kamal kiki
kamal kiki le 16 Fév 2012
Hi Walter Roberson
Can you please explain more the second part of your answer (starting from the floating point coefficients ), because I understood only the first part of your answer.

Connectez-vous pour commenter.


Alex Sha
Alex Sha le 8 Jan 2020
it is not easy to get correct initial start values, try to use global optimization algorithm instead of local ones like fsolve, refer to solution below:
x: 29.1663547800969
y: 246736.308525207
z: 279.389144571331

Catégories

En savoir plus sur Stability Analysis dans Help Center et File Exchange

Produits

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by