Nonlinear 3 equations 3 unknowns , hyperbolic, fsolve stopped because the last step was ineffective

I have 3 equations and 3 unknowns (x(1), x(2), and x(3)) which expressed in my objective function below:

function F2=F2(x)

F2(1)= 210+x(1)*asinh((sqrt((100^2/(x(1))^2)+(2*100/(x(1))))))-sqrt(100^2+2*x(1)*100)-x(3)

F2(2)= 210+x(2)*asinh((sqrt((100^2/(x(2))^2)+(2*100/(x(2))))))-sqrt(100^2+2*x(2)*100)+x(3)

F2(3)= 100000-981*x(1)+981*x(2)

end

then I recalled my initial guess of x(1) ; x(2); x(3) and try to solve it by this script in command window:

x0 = [150,5,15];

x = fsolve(@Obj,x0,optimset('disp','iter','LargeScale','off','TolFun',.01,'MaxFunEvals',1E5,'MaxIter',1E5))

but I got this following error message

No solution found.

fsolve stopped because the last step was ineffective. However, the vector of function
values is not near zero, as measured by the selected value of the function tolerance.

Anybody could give me some suggestion? I'm quite new in programming. and I did triple check about those three equation itself. Still no idea how I should approach this problem.

Regards,

Fredo Ferdian

criteria details

Answer 1

[Roger Stafford]

It is relatively easy to convert your three equations in three unknowns into a single equation in a single unknown. That would allow you to make a plot of the single equation’s expression as a function of the single unknown and determine visually the approximate point or points at which the curve crosses zero (assuming that ever happens.)

Add F2(1) and F2(2), which eliminates x(3). Then in F2(3) you can easitly solve for x(2) in terms of x(1) and substitute that for x(2) in the F2(2) expression. Now you are down to a single equation and the single unknown x(1). You can use ‘fzero’ to solve for it using the approximation(s) suggested from the plot. Once it is determined, it is then easy to find x(2) and x(3).

[fredo ferdian]

Thanks for your suggestion Roger Stafford, never think in that way.

I tried to do the approach as you said, and come up with single equation and single unknown then I got the x(2)by fzero command.

Since the x(2) already obtained, I calculate the x(1) based on F2(3) and get the x(3) based on F2(1)

but when I check all of the obtained unknown x(1),x(2),x(3), with F2(2), the equation doesn't work. (not resulting zero).

It's kind of weird. And the result of the unknown it self, is kind of far from value what I expected. Which part do you think I should look into? Or should I come back to my previous approach before (by using fsolve) ??

Thanks in advance!

Regards,

Fredo Ferdian

[Roger Stafford]

I assume you are looking for real-valued solutions, (as opposed to complex-valued ones.) If so, in order to avoid complex numbers, you must have x(2) >= -50 because of the expression

   sqrt(100^2+2*x(2)*100) = 10*sqrt(2)*sqrt(50+x(2))

and also because of the expression

   sqrt(100^2/x(2)^2+2*100/x(2)) = 
       10*sqrt(2)*sqrt((50+x(2))/x(2)^2)

Subject to this restriction I plotted the value F2(1)+F2(2) as a function of x(2) and its value never goes below 256, so, in particular, it doesn’t cross zero. That means there are no real-valued solutions to your equations.

If this is based on a real-life problem, presumably there has been some error in putting it into mathematical form. You had better review your thinking on these equations.

[fredo ferdian]

Yes indeed. I'm looking for real value solution. Ok then. I'll re-think the equation itself, and come back later if I can update the problem. Thanks anyway.

Regards,

Fredo Ferdian