Re: GSL 1.4: BUG #8 [rk8pd.c]

["MAISONOBE Luc" <luc dot maisonobe at c-s dot fr>]

Gerard Jungman a écrit :

> We have a subscription, but I don't seem to have
> access to electronic versions before 1995. So
> I will wander over to the library and see if
> it looks helpful. As you pointed out, the easiest
> thing to do might be to grab the numbers out of
> rksuite. I wouldn't trust anything printed in the
> journal, unless somebody out there can vouch for
> the accuracy. Has anybody listening here
> checked the numbers in the journal?

Since my last message on the subject 
(http://sources.redhat.com/ml/gsl-discuss/2002-q4/msg00020.html) I have 
check some of the coefficients.

As I said in that message, the article clearly says these numbers are 
approximations. The values from rksuite.f in Netlib are more accurate 
(Dormand and Prince seem to have provided better values to Brankin, 
Gladwell and Shampine).

I have tried to check these values using my rkcheck tool 
(http://www.spaceroots.org/software/rkcheck/index.html), and corrected 
some of them. Since Benoit's message yesterday, I have restarted this 
work and corrected more terms. What I mean here is *only* to replace 
float numbers with exact rational numbers, in order to check exactly the 
order. This is only of theoretical interest, for someone as picky as me 
;-) the values provided in the article are accurate to about 17 digits 
(just have a look to the first coefficients I corrected in my message 
last year) and the values in rksuite are accurate to about 30 digits. My 
 rational number are *not* better than this ones, they only form a 
globally consistent set, using some values as free parameters (for 
example 5490023248/9719169821 which is exactly the same in the article 
and in rksuite) and computing the other ones by solving the conditions 
equations and the additional equations from the article). The rational 
numbers I have computed so far (all the vector elements and some matrix 
elements) sometime involve really huge integers (more than 130 digits).

Again, I don't think my work is of *practical* interest. It will only be 
an external validation (if I succeed ...). I will post the xml file with 
the exact coefficients when it will be ready (for the moment, the one 
you can find at my site only contains the coefficients I had last year, 
i.e. the float values from rksuite and the two corrected rationals from 
my patch).

I am not subscribed to gsl list anymore, so this message will probably 
bounce. If either Gerard or Benoit think it could interest the list, 
please forward it by yourself.

Apart for Benoit :

I have brought the article to work this morning, if you want a copy, 
send me directly a postal adress or a fax number, and I will be happy to 
send you one.

                                                        Luc