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From: Thiago Oliveira on 30 Jul 2010 12:33
And more....

Without pdepe...is there another function suitable to solve hyperbolic equations?

Best Regards

Thiago Oliveira

"Thiago Oliveira" <thiagowsousa(a)gmail.com> wrote in message <i2uub4$ba3$1(a)fred.mathworks.com>...
> Torsten,
>
> Sorry by my mistakes...
>
> You're completely right about your comments...
>
> This pdepe function isn't suitable to hiperbolic equations....
>
> And the article that I read maybe was talking about the pde tool......
>
> Do you know something about the pde tool to solve this kind of problem?
>
> Best Regards and again, sorry by my mistakes
>
> Thiago
>
> Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <360018553.27787.1280490065383.JavaMail.root(a)gallium.mathforum.org>...
> > > Thanks for help Torsten,
> > >
> > > but I already solve this problem without
> > > "(1/Constant) * d^2T/dZ^2" term, that represent axial
> > > conduction using pdepe.
> > >
> >
> > That's clear. Without axial conduction, you can interpret
> > the axial variable as time variable. But
> > incorporating 'backmixing in time' is impossible.
> >
> > > I read in manual that pdepe is suitable to solve
> > > problems in 2D and hyperbolic equations, but I'm not
> > > so experienced on that function, so I dont know how
> > > to use it in that case.... :(
> >
> > I would be surprised if this is the case.
> > The 'pe' in pdepe stands for parabolic-elliptic -
> > and these are the problem types pdepe is designed for.
> > Maybe you read about the pde toolbox.
> >
> > >
> > > Anyway, thanks a lot for your help!
> > >
> > > I am still waiting for the solution! :)
> > >
> > > Best Regards
> > >
> > > Thiago
> > >
> > >
> >
> > Best wishes
> > Torsten.
> >
> > >
> > > Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote
> > > in message
> > > <1083225386.26679.1280471674680.JavaMail.root(a)gallium.
> > > mathforum.org>...
> > > > > hi everybody
> > > > >
> > > > > I'm trying to use the function pdepe for this
> > > > > equation:
> > > > >
> > > > > [1 - x^2]*dT/dZ = [(1/x)*d/dx*(x*dT/dx) +
> > > > > (1/Constant) * d2T/dZ]
> > > > >
> > > > > This equation represent a heat equation (forced
> > > > > convection)
> > > > >
> > > > > I already solve this equation making some
> > > > > simplifications, so it was turned in a parabolic
> > > > > equation.
> > > > >
> > > > > But that form represent a hyperbolic equation and
> > > I
> > > > > am not knowing how I put this equation on pdepe
> > > > > form....
> > > > >
> > > > > Can anyone help me to solve this problem?
> > > > >
> > > > > Best Regards
> > > > >
> > > > > Thiago
> > > >
> > > > If you mean
> > > > [1 - x^2]*dT/dZ = [(1/x)*d/dx*(x*dT/dx) +
> > > > (1/Constant) * d^2T/dZ^2] :
> > > > this is a stationary convection-diffusion equation
> > > > in 2d.
> > > > Since pdepe is only suited to solve 1d-problems,
> > > > you will have to use a different program to solve
> > > it.
> > > >
> > > > Best wishes
> > > > Torsten.
From: Torsten Hennig on 31 Jul 2010 02:35
> And more....
>
> Without pdepe...is there another function suitable to
> solve hyperbolic equations?
>
> Best Regards
>
> Thiago Oliveira
>

For hyperbolic pdes, there is no adequate tool in matlab.
You can try

http://www.amath.washington.edu/~claw/

but the pde you posted is not really hyperbolic.
Only similar to hyperbolic if the convective
part becomes dominant.

Best wishes
Torsten.
From: Torsten Hennig on 31 Jul 2010 02:39
> Torsten,
>
> Sorry by my mistakes...
>
> You're completely right about your comments...
>
> This pdepe function isn't suitable to hiperbolic
> equations....
>
> And the article that I read maybe was talking about
> the pde tool......
>
> Do you know something about the pde tool to solve
> this kind of problem?
>
> Best Regards and again, sorry by my mistakes
>
> Thiago
>

I have no experience with the pde toolbox, but
according to the documentation, it only seems
to be suitable for equations in pure elliptic,
hyperbolic or parabolic form.

Your convection-diffusion equation is a 'mixture'
between elliptic and hyperbolic.

Maybe you will need to discretize your equation by
finite differences and solve the resulting
system of nonlinear equations by the use of
MATLAB's FSOLVE.

Best wishes
Torsten.
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