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devel / comp.lang.fortran / Re: Bulirsch???Stoer vs Runge-Kutta

SubjectAuthor
* Bulirsch???Stoer vs Runge-KuttaMarco Aurelio Amarante Ribeiro
`* Bulirsch???Stoer vs Runge-KuttaThomas Koenig
 +- Bulirsch???Stoer vs Runge-KuttaMarco Aurelio Amarante Ribeiro
 `- Bulirsch???Stoer vs Runge-KuttaMarco Aurelio Amarante Ribeiro

1
Re: Bulirsch???Stoer vs Runge-Kutta

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Subject: Re: Bulirsch???Stoer vs Runge-Kutta
From: marcoaurelioamaranteribeiro@gmail.com (Marco Aurelio Amarante Ribeiro)
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 by: Marco Aurelio Amaran - Fri, 28 Oct 2022 14:55 UTC

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

Re: Bulirsch???Stoer vs Runge-Kutta

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From: tkoenig@netcologne.de (Thomas Koenig)
Newsgroups: comp.lang.fortran
Subject: Re: Bulirsch???Stoer vs Runge-Kutta
Date: Fri, 28 Oct 2022 17:30:42 -0000 (UTC)
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 by: Thomas Koenig - Fri, 28 Oct 2022 17:30 UTC

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).

Re: Bulirsch???Stoer vs Runge-Kutta

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Subject: Re: Bulirsch???Stoer vs Runge-Kutta
From: marcoaurelioamaranteribeiro@gmail.com (Marco Aurelio Amarante Ribeiro)
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 by: Marco Aurelio Amaran - Fri, 11 Nov 2022 12:03 UTC

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

Re: Bulirsch???Stoer vs Runge-Kutta

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Subject: Re: Bulirsch???Stoer vs Runge-Kutta
From: marcoaurelioamaranteribeiro@gmail.com (Marco Aurelio Amarante Ribeiro)
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 by: Marco Aurelio Amaran - Fri, 11 Nov 2022 12:07 UTC

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.

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