Equ-System how to solve?

[wschrabi-disabl]

Here would be my last and second problem in my recent project: How to solve a equ-sys with 4 unknown? Can anyone here give me some advice how it is done. I think it is only possible in an numerically way, right? Thanks for help.

[ptc-1368288]

On 2/27/2009 10:05:38 AM, wschrabi wrote:
>Here would be my last and
>second problem in my recent
>project: How to solve a
>equ-sys with 4 unknown? Can
>anyone here give me some
>advice how it is done. I think
>it is only possible in an
>numerically way, right? Thanks
>for help.
_______________________________

Not too easy as it looks.

You must cope between what makes the system
and what concludes the system or results from it.

jmG

[wschrabi-disabl]

I could discover, that I used 4 Equs for just 3 variables. (There was a mistake in the Equs.tt=tau) I have attached the new sheet and the solution from Maple. Maple takes just 5 sec to solve. How is it done in Mathcad?
Is it possible to make Substitutions with part or the N1 definition in the solver-Block? THe N1 Definition is sooooo long (see txt file) when you put all substitutes in the formular.

[TomGutman]

Your comment lists t as one of the unkowns. Your find statement has tt as one of the unkowns. But the equations in the solve block have neither t nor tt. You cannot solve for something that is not in the equations -- ain't gonna work.
__________________
� � � � Tom Gutman

[wschrabi-disabl]

Thanks here the corrected version, could do it, but there is still a bug in it. I can not find it.
Or is that only the accuracy?

[TomGutman]

No way am I going to try to decipher that monstrous equation. But I do note that you have N1 and N1q which have vastly different values. That would indicate that your guess values are way off.

Also, note that you are working from several sources, and they are not necessarily consistent with each other as to their usage of names. As I remember, one of the papers did the ODE strictly in terms of quantities, without any explicit reference to volumes (except for the initial conditions), while another one did it in terms of concentration with volumes explicitly included. The k values used in these formulations are not necessarily the same.
__________________
� � � � Tom Gutman

[wschrabi-disabl]

I have just uploaded a corr. version. The monster equ should be correct. But you are right, I had some troubles with concentration[mg/l] and mass[mg]. But I think that I have solve, don`t I?

Thanks for your comment. Yes, that is now clear, the k-s are not the same from the ODE as there was concentration [mg/l] and the N-lambda Model uses mass[mg]. I have added the verification from the Inusoft Prg. It is the same. Now I am satisfied. Thanks a lot for your help.

[ptc-1368288]

On 2/27/2009 3:33:46 PM, wschrabi wrote:
>I have just uploaded a corr.
>version. The monster equ
>should be correct. But you are
>right, I had some troubles
>with concentration[mg/l] and
>mass[mg]. But I think that I
>have solve, don`t I?
Thanks
>for your comment. Yes, that is
>now clear, the k-s are not the
>same from the ODE as there was
>concentration [mg/l] and the
>N-lambda Model uses mass[mg].
>I have added the verification
>from the Inusoft Prg. It is
>the same. Now I am satisfied.
>Thanks a lot for your help.
_____________________________

That was noticed but it does not matter as the system works in the scalar domain. If something needs be converted back, it's after. In the infectious model, there are no partial dead and the system has like this one: fractional parameters. The Logis-fit is in the transform domain, as well as the exact solution. However there may be a point to consider.

jmG

[ptc-1368288]

On 2/27/2009 2:59:50 PM, wschrabi wrote:
>Thanks here the corrected
>version, could do it, but
>there is still a bug in it. I
>can not find it.
Or is that
>only the accuracy ?
______________________________

I have added a note in grey, please read not too fast. k01, k12, k21 are the rate coefficients in the DE system, they are scalar, they only belong to the DE system. What you have done via the "monstrous equation" are not scalar to the DE system , they are scalar to the domain of the fit function. Bug or not, that you have to check, but for sure your very last k01, k12, k21 have same parenthood to the DE system like a cat and a carrot.

Everything is right one way or another except the INUsoft plot and this one don't match. Accordingly to what you explained me before , the INUsoft plot is wrong or partial and maybe not the last part of their report. Their work is not traceable to my taste, but their report and our work corroborate for the fit to the experimental or otherwise estimated project. Both fits agree. The exact fit is another matter and a matter of preference after you have done such a great job putting it right and executable to match the numerical DE, but it is an exact fit to the numerical DE only and it can't be otherwise because you don't have a true data set resulting from a function.
It might sound dense for the non familiar, but at the stage you are it should be clear like the day. Please feel free for more clarification.

jmG

[ptc-1368288]

... from the engineering point of designing such a system and trying to "control" it, it's possible to consider both V1 & V2 of different capacity by controlling the level in each, but the system would be floating around like a dog chasing his tail. Fixing V2 is much easier and should be fixed. What's coming into the system is much easier to control immediately, i.e: calculate V1 and consequently control the level in V1. A control scheme would imply to control the quality flow rate k12, k21, maintain the V1 by level control and cascading k12, k21 from the outlet k01 quality flow... 4 control loops. The parameters in the control loops k12, k21, k01 are just numbers that belong this time to the "control domain".

Each serious project require aging, like wine.

jmG

[ptc-1368288]

...simplify "Monster Inc",
check, it works fine !



jmG

[wschrabi-disabl]

How did you do the simplification? In Maple I get following simpified N1: (general) Moreover I could calculate with Maple the symb Solution of this Equ Sys. What does the RootOf() mean? Are these the roots of this function? And what means _Z in that solution? Can anyone this explain?

I have attached the *.txt File with the symbolic solution from Maple.

NA = N1,
ALA1 = lambda1
ALA2 = lambda2

Tks

[wschrabi-disabl]

I can not see your gifs in the next 3 postings. Here I have add some remarks due to the diff. k-values.(before I have read your posting)