Ahh. I missed that. FindRoot(ES1).smz (4kb) downloaded 27 time(s).

Hello ola_nicolas,

My advice to you is to try changing the units of your known variables (if this can have a physical meaning, of course) in order to get the solution of unknown variables not so close to zero. And every time check the solution - surprises are always possible.

Regards,
Radovan

Hello everybody

Thanks Jean Giraud for the alert. Thanks Radovan for advice. Thank you all for your involvement. Without you it could not have been a convenient solution. Radovan is right. I have made ab initio the transformations in the units of measurement that I use in practice. I will do more tests and checks until I have established the usable form of the solution. However, from the point of view of the result, I find myself close to physical reality. Thank you once again.

Post scriptum: Please tell me what kind of files are those with the ending "msz". I have tried unsuccessfully to open the files posted by ElSid.

Edited by user 20 March 2018 09:42:41(UTC)  | Reason: Not specified

Auguri Davide

Thank you for your answer. I do not have time now, but I will try later to see how I have to do it. Otherwise, all the best.

Greetings to all

In attachment I intend to do a comparative study between solving the equation system using different units of measure. The first variant is the one already previously analyzed, with the measurement units dictated by practical considerations - [Hz] for frequencies, [T] for inductions and [W / mm3] for specific losses in the magnetic core. The following three variants correspond to the set of measuring units - [kHz] for frequencies, [T] for inductions and [kW / m3], used in ferrite cores producers data sheets. It is seen that depending on the set of three initial data, the result of the calculation is altered in variants 3 and 4. I also responded to Radovan's request to try to use different measurement units in order to avoid the zero convergence of the solutions for the variables η si λ. It can be seen that the use of this set of units of measure has advantages over the other. Considering the very wide range of ferrite cores currently produced, it is very likely that in some cases the calculation will yield vague results.

On the other hand, in connection with Radovan's fear that the use of very small subunits can affect the calculation, I think it is unreasonable. I made a SMath spreadsheet to see what result returns my program to 1/10^308. It was 10^-308. So in numerical representation, the program can distinguish between extremely close to zero results. By comparison, MathCAD has set the ∞ (infinite) level of 10^307. At the same time, however close to zero, the result does not in any way affect my initial values ​​set for the variables. The difference between the value returned by calculating of two variables, and their initial value, will always be less than the unit. For the value of exponent n, in practice we find values ​​of the order of the result from this calculation. So it seems to me that the advantage of the first option is obvious. Otherwise, all the best.

Using different units for the equations in FindRoot(2) essentially means to use different relative convergence criteria if these aren't adjusted in the FindRoot() call.

FindRoot() internally converts the numbers to base units (meter). The default tolerance of 0.0001 for variable and function is to be interpreted in the base unit of the given quantity.

In the first example with volume and height being close to unity in base units, the default tolerance is appropriate.
If the dimensions are scaled by factor 0.001 (mm instead of m) then the tolerance is nearly of the same magnitude as the variable. The result is complete rubbish. The problem is fixed by adjustment of the tolerances.


findroot.sm (30kb) downloaded 13 time(s).

Hi



All right, I think I understand. Corroborating Martin's information with Jean Giraud's example (using graphical representations) I understand it is possible that the function passes through the points I choose to apply the FindRoot procedure, while the rest of the points are quite far from what they should results using the negligible tolerances in relation to the magnitude of variables. I will study much more carefully these numerical procedures for solving equations and / or systems of equations. Thank you all.