Em domingo, 6 de março de 2011 às 06:18:29 UTC-3, glen herrmannsfeldt escreveu:
> nm...@cam.ac.uk wrote:
> (snip on integration algorithms)
> > Rather longer ago that that, I was working on multi-dimensional
> > scaling, which has the property that it has a set of fairly
> > well-defined local minima, but where discontinuities are dense
> > (but in the same direction as the slope). Steepest descents
> > worked; little else did.
> > There is a fairly general rule that the less well-behaved the
> > problem you have, the cruder a method you must use, because all
> > fancy methods need to make more assumptions. Runge-Kutta is a
> > bit odd, but also blows up quite spectacularly given a hostile
> > enough function. For some, there is little option but simple
> > step-by-step approximation.
> I always liked Gaussian quadrature, though its assumptions
> likely cause problems with some functions. With no prediction,
> it shouldn't get too confused. The old trick of running with
> different order and checking that the result isn't too different
> should still work.
> > As a side-note, IBM SSP contained the only matrix inversion code
> > that I have ever seen that succeeded in inverting a singular 3x3
> > matrix - AND returning elements of the same order as the input!
> > Impressive.
> The code is still around, if anyone wants to try it.
> > Harwell and NAG didn't like the matrix at all :-)
> -- glen

I would like to present my article to the group:

https://brazilianjournals.com/ojs/index.php/BRJD/article/view/46840

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On Friday, August 5, 2022 at 1:51:03 PM UTC+2, Marco Amarante wrote:
....
> I would like to present my article to the group:
>
> https://brazilianjournals.com/ojs/index.php/BRJD/article/view/46840
> --
>
You do not happen to have an English version of it? My understanding of Portuguese is rather limited, even though I can of course recognise the equations ;).

Regards,

Arjen

Em sexta-feira, 5 de agosto de 2022 às 11:41:56 UTC-3, arjen.m...@gmail.com escreveu:
> On Friday, August 5, 2022 at 1:51:03 PM UTC+2, Marco Amarante wrote:
> ...
> > I would like to present my article to the group:
> >
> > https://brazilianjournals.com/ojs/index.php/BRJD/article/view/46840
> > --
> >
> You do not happen to have an English version of it? My understanding of Portuguese is rather limited, even though I can of course recognise the equations ;).
>
> Regards,
>
> Arjen

--

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IMPRIMIR.

"Responsabilidade com o MEIO AMBIENTE"

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quaisquer arquivos em anexo podem conter informações confidenciais e/ou
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Em sexta-feira, 5 de agosto de 2022 às 11:41:56 UTC-3, arjen.m...@gmail.com escreveu:
> On Friday, August 5, 2022 at 1:51:03 PM UTC+2, Marco Amarante wrote:
> ...
> > I would like to present my article to the group:
> >
> > https://brazilianjournals.com/ojs/index.php/BRJD/article/view/46840
> > --
> >
> You do not happen to have an English version of it? My understanding of Portuguese is rather limited, even though I can of course recognise the equations ;).
>
> Regards,
>
> Arjen

Arjen

I can write an English version of it if participants are interested

Regards, ,

Marco Aurelio Amarante Ribeiro

--

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On Friday, August 19, 2022 at 6:24:43 PM UTC+2, Marco Amarante wrote:
> Em sexta-feira, 5 de agosto de 2022 às 11:41:56 UTC-3, arjen escreveu:
> > On Friday, August 5, 2022 at 1:51:03 PM UTC+2, Marco Amarante wrote:
> > ...
> > > I would like to present my article to the group:
> > >
> > > https://brazilianjournals.com/ojs/index.php/BRJD/article/view/46840
> > > --
> > >
> > You do not happen to have an English version of it? My understanding of Portuguese is rather limited, even though I can of course recognise the equations ;).
> >
> > Regards,
> >
> > Arjen
> Arjen
>
> I can write an English version of it if participants are interested
>
> Regards, ,
>
That might be interesting indeed :).

Regards,

Arjen

On Monday, August 22, 2022 at 4:43:04 PM UTC+2, Arjen Markus wrote:

> >
> > I can write an English version of it if participants are interested
> >
> > Regards, ,
> >
> That might be interesting indeed :).
>
> Regards,
>
> Arjen

On Wikipedia I found a short description of the method with several caveats: according to some authors there is little to gain with the techniques that Bulirsch-Stoer depends on. Do you share that conclusion?

Regards,

Arjen

In article <bdfb06b3-90b3-40a8-94d3-42a0b99672bcn@googlegroups.com>,
Arjen Markus <arjen.markus895@gmail.com> writes:

> On Monday, August 22, 2022 at 4:43:04 PM UTC+2, Arjen Markus wrote:
>
> > >
> > > I can write an English version of it if participants are interested
> > >
> > > Regards, ,
> > >
> > That might be interesting indeed :).
> >
> > Regards,
> >
> > Arjen
>
> On Wikipedia I found a short description of the method with several
> caveats: according to some authors there is little to gain with the
> techniques that Bulirsch-Stoer depends on. Do you share that conclusion?

I once coded a real-world application where Bulirsch-Stoer worked better
than Runge-Kutta (though using polynomial rather than rational-function
extrapolation).

I think that Bulirsch-Stoer is one of the great ideas of numerical
analysis.

On Thursday, September 1, 2022 at 1:28:55 AM UTC-7, Phillip Helbig (undress to reply) wrote:

(snip)

> I think that Bulirsch-Stoer is one of the great ideas of numerical
> analysis.

I used to know some of this, but I forget now.

The only one I remember is that higher than 4th order Runge-Kutta
isn't better, in terms of step size and number of function evaluations.

With small enough step size, it doesn't make so much difference.

gah4 <gah4@u.washington.edu> schrieb:
> On Thursday, September 1, 2022 at 1:28:55 AM UTC-7, Phillip Helbig (undress to reply) wrote:
>
> (snip)
>
>> I think that Bulirsch-Stoer is one of the great ideas of numerical
>> analysis.
>
> I used to know some of this, but I forget now.
>
> The only one I remember is that higher than 4th order Runge-Kutta
> isn't better, in terms of step size and number of function evaluations.

This really depends.

If you are trying to integrate x'' + x = 0, as smooth as you can
get, then higher order will help.

If your function is less well behaved, then lower order will be
better, and if your system of equations is stiff, you will have
to use quite different solvers.

> With small enough step size, it doesn't make so much difference.

Unless you make it too small and get cancellation in your
difference quotients :-)

Em quinta-feira, 1 de setembro de 2022 às 13:50:53 UTC-3, Thomas Koenig escreveu:
> gah4 <ga...@u.washington.edu> schrieb:
> > On Thursday, September 1, 2022 at 1:28:55 AM UTC-7, Phillip Helbig (undress to reply) wrote:
> >
> > (snip)
> >
> >> I think that Bulirsch-Stoer is one of the great ideas of numerical
> >> analysis.
> >
> > I used to know some of this, but I forget now.
> >
> > The only one I remember is that higher than 4th order Runge-Kutta
> > isn't better, in terms of step size and number of function evaluations.
> This really depends.
>
> If you are trying to integrate x'' + x = 0, as smooth as you can
> get, then higher order will help.
>
> If your function is less well behaved, then lower order will be
> better, and if your system of equations is stiff, you will have
> to use quite different solvers.
> > With small enough step size, it doesn't make so much difference.
> Unless you make it too small and get cancellation in your
> difference quotients :-)

hello everyone
I have one plus one article using the
Bulirsch–Stoer:
https://gjeta.com/content/pollutant-dispersion-modeling-lakes-interconnected-channels-solution-using-bulirsch-stoer

Marco Aurelio Amarante Ribeiro <marcoaurelioamaranteribeiro@gmail.com> schrieb:
> Em quinta-feira, 1 de setembro de 2022 às 13:50:53 UTC-3, Thomas Koenig escreveu:
>> gah4 <ga...@u.washington.edu> schrieb:
>> > On Thursday, September 1, 2022 at 1:28:55 AM UTC-7, Phillip Helbig (undress to reply) wrote:
>> >
>> > (snip)
>> >
>> >> I think that Bulirsch-Stoer is one of the great ideas of numerical
>> >> analysis.
>> >
>> > I used to know some of this, but I forget now.
>> >
>> > The only one I remember is that higher than 4th order Runge-Kutta
>> > isn't better, in terms of step size and number of function evaluations.
>> This really depends.
>>
>> If you are trying to integrate x'' + x = 0, as smooth as you can
>> get, then higher order will help.
>>
>> If your function is less well behaved, then lower order will be
>> better, and if your system of equations is stiff, you will have
>> to use quite different solvers.
>> > With small enough step size, it doesn't make so much difference.
>> Unless you make it too small and get cancellation in your
>> difference quotients :-)
>
> hello everyone
> I have one plus one article using the
> Bulirsch–Stoer:
> https://gjeta.com/content/pollutant-dispersion-modeling-lakes-interconnected-channels-solution-using-bulirsch-stoer

This particular problem (basically three stirred tanks with
volume flow between them, assumed to be perfectly mixed, with
flows between them) lends itself to an analytical solution.
The eigenvalues of a 3*3 matrix are not that hard to determine,
and an analytical solution could also give you a frequency
response (for example).

Em sexta-feira, 28 de outubro de 2022 às 14:30:46 UTC-3, Thomas Koenig escreveu:
> Marco Aurelio Amarante Ribeiro <marcoaurelioa...@gmail.com> schrieb:
> > Em quinta-feira, 1 de setembro de 2022 às 13:50:53 UTC-3, Thomas Koenig escreveu:
> >> gah4 <ga...@u.washington.edu> schrieb:
> >> > On Thursday, September 1, 2022 at 1:28:55 AM UTC-7, Phillip Helbig (undress to reply) wrote:
> >> >
> >> > (snip)
> >> >
> >> >> I think that Bulirsch-Stoer is one of the great ideas of numerical
> >> >> analysis.
> >> >
> >> > I used to know some of this, but I forget now.
> >> >
> >> > The only one I remember is that higher than 4th order Runge-Kutta
> >> > isn't better, in terms of step size and number of function evaluations.
> >> This really depends.
> >>
> >> If you are trying to integrate x'' + x = 0, as smooth as you can
> >> get, then higher order will help.
> >>
> >> If your function is less well behaved, then lower order will be
> >> better, and if your system of equations is stiff, you will have
> >> to use quite different solvers.
> >> > With small enough step size, it doesn't make so much difference.
> >> Unless you make it too small and get cancellation in your
> >> difference quotients :-)
> >
> > hello everyone
> > I have one plus one article using the
> > Bulirsch–Stoer:
> > https://gjeta.com/content/pollutant-dispersion-modeling-lakes-interconnected-channels-solution-using-bulirsch-stoer
> This particular problem (basically three stirred tanks with
> volume flow between them, assumed to be perfectly mixed, with
> flows between them) lends itself to an analytical solution.
> The eigenvalues of a 3*3 matrix are not that hard to determine,
> and an analytical solution could also give you a frequency
> response (for example).

Daniel(dcar...@gmail.com),
sorry for the delay in responding. In my master's thesis, I answer your question. See the link.

https://sucupira.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=11494524

Em sexta-feira, 28 de outubro de 2022 às 14:30:46 UTC-3, Thomas Koenig escreveu:
> Marco Aurelio Amarante Ribeiro <marcoaurelioa...@gmail.com> schrieb:
> > Em quinta-feira, 1 de setembro de 2022 às 13:50:53 UTC-3, Thomas Koenig escreveu:
> >> gah4 <ga...@u.washington.edu> schrieb:
> >> > On Thursday, September 1, 2022 at 1:28:55 AM UTC-7, Phillip Helbig (undress to reply) wrote:
> >> >
> >> > (snip)
> >> >
> >> >> I think that Bulirsch-Stoer is one of the great ideas of numerical
> >> >> analysis.
> >> >
> >> > I used to know some of this, but I forget now.
> >> >
> >> > The only one I remember is that higher than 4th order Runge-Kutta
> >> > isn't better, in terms of step size and number of function evaluations.
> >> This really depends.
> >>
> >> If you are trying to integrate x'' + x = 0, as smooth as you can
> >> get, then higher order will help.
> >>
> >> If your function is less well behaved, then lower order will be
> >> better, and if your system of equations is stiff, you will have
> >> to use quite different solvers.
> >> > With small enough step size, it doesn't make so much difference.
> >> Unless you make it too small and get cancellation in your
> >> difference quotients :-)
> >
> > hello everyone
> > I have one plus one article using the
> > Bulirsch–Stoer:
> > https://gjeta.com/content/pollutant-dispersion-modeling-lakes-interconnected-channels-solution-using-bulirsch-stoer
> This particular problem (basically three stirred tanks with
> volume flow between them, assumed to be perfectly mixed, with
> flows between them) lends itself to an analytical solution.
> The eigenvalues of a 3*3 matrix are not that hard to determine,
> and an analytical solution could also give you a frequency
> response (for example).

Thomas Koenig

Really this specific problem can be solved by an EDO's that have analytical solutions, as the article showed. Thank you for your participation.