Re: Reliability?

From: Repeating Rifle (salmonegg_at_sbcglobal.net)
Date: 09/20/04 

Date: Mon, 20 Sep 2004 21:18:39 GMT

in article cin938$1gp8$1@ns.felk.cvut.cz, Michal Kvasnicka at
michal.kvasnicka@No_s_Pam.quick.cz wrote on 9/20/04 11:55 AM:

> In fact, I am looking for suitable tool which is able to reliable solve
> SYMBOLICALLY the large system of linear 1st order ODEs (100-1000 eqs.) with
> constant coefficients. The coefficients are numerical float values.
>
> The main reason for symbolic solution is the extremely large range of
> coefficients values (1-10^15), which can produce terrible numerical
> instabilities or losses of accuracy. Due to this fact, I would like to try
> numerically evaluate final solution of the system of ODEs instead of direct
> numerical solution of the whole system.

I must first point out that I am not Maple proficient.

The task you face is exactly that of traditional electric circuit analysis.
There are solvers available for stiff ODEs that have looked into the
problems you describe.

In the end, when it comes to getting the eigenvalues of your large matrix,
you will not be able to do so except numerically. I believe that there is no
symbolic general solution available for algebraic equations of the fifth
degree or higher. Your indicial equation degree will be many times too
large.

Bill