Re: Solving PDE; novice question

[John B. Thoo]

On Apr 13, 2009, at 9:58 PM, John B. Thoo wrote:

> Hello, everyone.
>
> I've had Octave loaded on my PowerBook for a long time (v. 2.1.73)
> and have used it *very* lightly for very simple things, mostly to
> obtain simple plots.  Now I have a good reason to upgrade Octave and
> learn to use it better: I need to solve a PDE.  Henry Mollet sent me
> instructions on upgrading to v. 3.x some time ago and I've kept those
> instructions, so I can upgrade.  (Thanks, Henry!) :-)
>
> Now my questions.  The questions are about Octave, but please note
> that I don't have any experience with numerics or coding at all, so
> please be gentle.
>
> 1)  Can Octave be used to solve an equation like this:
>
>    u_{tt}(x,t) - C * u_{xx}(x,t)
>    = B * \int_{-infty}^{+\infty} K(x-y,y) * u(x-y,t) * u(y,t) dy,
>
> where  B, C  are constants and  K  is some kernel.
>
> 2) If the answer is yes, then where should I look in the
> documentation (or elsewhere) to learn (in baby steps) how to solve
> such an equation eventually?  (I think one good step along the way,
> after some initial baby steps solving some baby equations, would be
> to solve the inviscid Burgers equation:
>
>    u_t + u*u_x = 0,  u = u(x,t).)
>
> Thanks for your help.
>
> ---John.
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> address@hidden
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On Apr 15, 2009, 05:43am, martin helm wrote:

> Carlo de Falco-2 wrote:
>
> On 15 Apr 2009, at 00:18, Ivan Sutoris wrote:
>
> > I'm not expert on PDE's, but I think Octave itself does not have
> > specific function for PDE solving, and I don't see such package at
> > Octave-Forge either. I've discovered some finite element code for
> > Octave on the web [1], [2] , but haven't tried it myself.
> >
> > [1] FEMOCTAVE: http://ideas.repec.org/c/cod/octave/c090801.html
> > [2] OctMesh: http://octmesh.forja.rediris.es/
>
> Among packages devoted to solution of  PDEs in general, I'd like to
> mention, in addition to the ones above,
> the octave-forge package BIM
>
> [3] BIM: http://octave.sourceforge.net/bim
>
> but, to my knowledge, none of the above can deal out of the box with
> the kind of non-linear integro-differential problem mentioned by th OP
>
> > Regards
> > Ivan Sutoris
>
> c.
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> «  [hide part of quote]
> So far I know not directly an octave package for conservation laws.
> If you are interested in introductory code (as I understand your  
> question),
> to start your own octave coding for the equations you mentioned  
> have a look at
>
> http://www.math.toronto.edu/mpugh/Teaching/Mat1062/mat1062.html
>
> especially
>
> http://www.math.toronto.edu/mpugh/Teaching/Mat1062/ 
> conservation_laws.html
>
> (There are some simple .m files which should directly work with  
> octave).
>
> There exists also some code for matlab to solve burger's equation at
>
> http://www.mathworks.com/matlabcentral/fileexchange/11101
>
> but this one needs some rework for octave since it uses ode15s  
> (which is not in octave).
>
> - mh

First, thank you, Ivan, Carlo, and Martin, for your replies.

Off topic:  My original post arrived from the listserv in my email  
mailbox as expected, but I never received any of your replies in my  
mailbox.  Later, I went to the Octave web site to search the help  
archives and, lo, I see your three replies to my query even though I  
still haven't received any of these responses in my email mailbox.  I  
am continuing to receive postings to the help-octave listserv on  
other topics from others in my email mailbox, but none of the replies  
to my own query.  What am I doing wrongly?  Had I not happened to try  
to search the help archive, I would not have seen the responses.

On topic:  Thanks for all the links.  In addition, when I googled  
"solving pde with octave", I found [4].  But, after reading the  
installation notes on the web page, I'm not sure if I can or how to  
install the package on my PowerBook.

[4] <http://waxworksmath.com/Software/pdeone_rkc.html>

I will look at [1, 2, 3], but I'm not sure that I will be able to  
make heads or tails of them, yet.  Where I've started is to read Mary  
Pugh's lecture notes that Martin referenced above to try to orient  
myself.  Then I will try to dive into something.

If anyone has any advice on how I, who have never really done any  
numerics, can learn in short order what's necessary to lead me to  
solving my problem, please shoot it my way.  Thanks very much to  
everyone.

---John.