Sturm-Liouville (eigenvalue/eigenfunction) problems

Alan

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Jun 20, 2006, 2:25:20 AM6/20/06

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Anyone know some available Mathematica sources
for these problems on a finite interval?

Thanks!
alan

Selwyn Hollis

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Jun 21, 2006, 2:41:42 AM6/21/06

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Alan,

Here's a link to a notebook containing some sample material on
Fourier series and Sturm-Liouville eigenvalue problems from my book A
Mathematica Companion for Differential Equations:

http://tinyurl.com/e8cmp

It contains a number of good examples beyond the usual boring ones
with constant coefficients.

I hope it's useful.

-- Selwyn Hollis

Alan

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Jun 23, 2006, 4:39:01 AM6/23/06

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"Selwyn Hollis" <sh2....@earthlink.net> wrote in message
news:e7apn6$99s$1...@smc.vnet.net...
> Alan,

> It contains a number of good examples beyond the usual boring ones
> with constant coefficients.
>
> I hope it's useful.
>
> -- Selwyn Hollis

Thanks for the notebook, Selwyn.

Since my original post I have discovered the SLEIGN2
fortran package and ported the regular case to Mathematica.
It works fine so far on my application.

A good project for somebody's graduate student would be
to port the whole thing -- given Mathematica's superior
visualizations, I very surprised this hasn't been done.

I am also surprised there are no built-in methods for
this, given its importance to mathematics.

regards,
alan

jbak...@gmail.com

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Jul 6, 2006, 7:18:00 AM7/6/06

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I have just recently ported the regular case as well to Mathematica. I
did not port this directly from SLIEGN2, but rather used NDSolve with
the differential equations derived from Prufer Coordinates. I'm
familiar and have used SLEIGN2 as well.

I am interested in porting this to Mathematica. I'd enjoy some
collaboration, if you have time. I am a graduate student with
experience in programming. But not so much with Mathematica.

One question I do have - is what is your interest in using Mathematica
to solve SL problems??

Thanks,
Jeff Baker

Paul Abbott

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Jul 10, 2006, 7:14:09 AM7/10/06

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In article <e784cg$fo8$1...@smc.vnet.net>,
"Alan" <in...@optioncity.REMOVETHIS.net> wrote:

> Anyone know some available Mathematica sources
> for these problems on a finite interval?

There are many approaches to solving Sturm-Liouville problems in
Mathematica. Probably the most straightforward approach is to use
variational (or Galerkin) methods. For example, VariationalBound or
NVariationalBound in

<<Calculus`VariationalMethods`

give approximate eigenvalues and eigenfunctions.

As an aside, Trott outlines the inverse Sturm-Liouville problem in his
Symbolics Guidebook (pp 337-8).

Cheers,
Paul

_______________________________________________________________________
Paul Abbott Phone: 61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
The University of Western Australia (CRICOS Provider No 00126G)
AUSTRALIA http://physics.uwa.edu.au/~paul

Alan

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Jul 11, 2006, 6:11:41 AM7/11/06

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<jbak...@gmail.com> wrote in message news:e8irh8$sbq$1...@smc.vnet.net...

>I have just recently ported the regular case as well to Mathematica. I
> did not port this directly from SLIEGN2, but rather used NDSolve with
> the differential equations derived from Prufer Coordinates. I'm
> familiar and have used SLEIGN2 as well.
>
> I am interested in porting this to Mathematica. I'd enjoy some
> collaboration, if you have time. I am a graduate student with
> experience in programming. But not so much with Mathematica.
>
> One question I do have - is what is your interest in using Mathematica
> to solve SL problems??
>
> Thanks,
> Jeff Baker

Hi Jeff,

By 'porting the regular case', I meant exactly what you did: use NDSolve
with the Prufer variables. I haven't really looked at the SLEIGN Fortran.

My general interest is in quantitative finance applications. More
specifically I was
trying to understand the phenomenom of the blow-up of some
pde problems on the half-line through some regular SL approximations.

Feel free to email me directly.

regards,
alan