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List:       kde-devel
Subject:    Re: Kalamaris  Solution of Differential Equations by numerical
From:       Antonio Larrosa =?iso-8859-1?q?Jim=E9nez?= <larrosa () kde ! org>
Date:       2003-05-22 23:43:11
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El Sunday 18 May 2003 08:13, James Richard Tyrer escribió:
> I mentioned this project in my previous posting but couldn't remember
> it's name.

Hello, before I forget, please always use my larrosa@kde.org address.

>
> This application looks very good, but the important thing when solving
> DEs is getting good answers.  The homepage:

Yep,

>
> http://perso.wanadoo.es/antlarr/kalamaris.html

Use better http://developer.kde.org/~larrosa/kalamaris.html
which is a bit more updated (though I'm afraid there's not a new version 
yet).

> mentions using various methods.  I understood that these were being
> taught in a class that the programmer was taking.

Exactly,

> It is my understanding that the methods listed will all break when
> solving an ordinary second order DE with a solution of:

Probably, yes :)

> 	A*EXP(-K*T)
>
> 	A*EXP(-K*T)*SIN(2*PI*F*T)
>
> But I noticed that he asked only for help with:

Well, of course I just said those as examples, if you help in other areas 
you're also welcomed !

> My abilities are as I said, in numerical analysis.

Great, btw, are you a mathematician too ?

> The best way to solve DEs by numerical integration is with the method
> described in Numerical Methods that Work, by Acton Richardson  A
> method that will accurately and stably solve the above example.

I didn't know that method, but I'm of course happy to hear about it now
>
> http://mathworld.wolfram.com/RichardsonExtrapolation.html
>

Very interesting link, but I'm afraid it's not enough to implement that 
method (although Kalamaris already adjusts the step size during the 
calculation, but I suppose that page tries to say that the step size 
adjust is made in a special way). I'll try to ask my teachers about that 
Richardson book and see if I can find it. Anyway, I think the "Bulirsch 
and Stoer" book is in the library of my univ, so I'll have a look.

On the bad side, I'm afraid I'm really short on time lately, so I won't 
have visible results as soon as I'd like :-(

> Even though this method is much simpler to implement than the higher
> order methods based on the Runge-Kutta Algorithm it does not appear to
> be taught in basic numerical analysis courses.

That's really a pity, specially if it's easier to implement :)

Thanks for your ideas.

--
Antonio Larrosa Jimenez
KDE developer - larrosa@kde.org
http://developer.kde.org/~larrosa/
I contradict what I said because now I know better - Gandhi
 
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