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## Re: Solving PDE; novice question

 From: John B. Thoo Subject: Re: Solving PDE; novice question Date: Thu, 16 Apr 2009 07:57:54 -0700


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

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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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.



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