Solving PDE; novice question

[John B. Thoo-2]

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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[Ivan Sutoris]

On Tue, Apr 14, 2009 at 6:58 AM, John B. Thoo <JTHOO@...> 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.

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/

Regards
Ivan Sutoris

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[Carlo de Falco-2]

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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[martin_helm]

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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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

[John B. Thoo-2]

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.
> _______________________________________________
> Help-octave mailing list
> Help-octave@...
> https://www-old.cae.wisc.edu/mailman/listinfo/help-octave

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.
> _______________________________________________
> Help-octave mailing list
> Help-octave@...
> https://www-old.cae.wisc.edu/mailman/listinfo/help-octave
> «  [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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[sidd85]

Hey John,

it is definitely possible to solve such an equation with octave. But as far as I know there doesn't exist any toolbox for solving this out-of-the-box.
In my opinion the best thing to do is going to a library and reading about numerics of nonlinear pde's. I also think that anything from the web, e.g. sourcecodes, is not going to help you in the right way. If you plan to solve this equation, the problem won't be octave, matlab or any special program. It is the numerics.

Good luck,

Johannes