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From: Kate on 16 Jun 2010 11:28
I have a system of two PDE's, and I want to solve them over two different domains using pdepe. I need my first equation to be valid over [-.15,.2], but I want my second equation to be valid only over [0,.05]. Is there a way to define two different xmesh's so that this works?
From: Torsten Hennig on 16 Jun 2010 22:21
> I have a system of two PDE's, and I want to solve
> them over two different domains using pdepe. I need
> my first equation to be valid over [-.15,.2], but I
> want my second equation to be valid only over
> [0,.05]. Is there a way to define two different
> xmesh's so that this works?

... and the solution variables of the two equations
are somehow coupled ?

Best wishes
Torsten.
From: Kate on 17 Jun 2010 16:20
Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <1651498785.359498.1276755741438.JavaMail.root(a)gallium.mathforum.org>...
> > I have a system of two PDE's, and I want to solve
> > them over two different domains using pdepe. I need
> > my first equation to be valid over [-.15,.2], but I
> > want my second equation to be valid only over
> > [0,.05]. Is there a way to define two different
> > xmesh's so that this works?
>
> .. and the solution variables of the two equations
> are somehow coupled ?
>
> Best wishes
> Torsten.

Yes. The second equation is independent and can be solved independently, but the first depends on the second.
From: Torsten Hennig on 17 Jun 2010 22:27
> Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote
> in message
> <1651498785.359498.1276755741438.JavaMail.root(a)gallium
> .mathforum.org>...
> > > I have a system of two PDE's, and I want to solve
> > > them over two different domains using pdepe. I
> need
> > > my first equation to be valid over [-.15,.2], but
> I
> > > want my second equation to be valid only over
> > > [0,.05]. Is there a way to define two different
> > > xmesh's so that this works?
> >
> > .. and the solution variables of the two equations
> > are somehow coupled ?
> >
> > Best wishes
> > Torsten.
>
> Yes. The second equation is independent and can be
> solved independently, but the first depends on the
> second.

If you want to use pdepe, I only see the following way to go:
1. Solve the second equation and store data needed for the first equation at different output times.
2. Solve the first equation and use the previously saved data. If data are needed at times where you did not
store the solution of the first equation, use interpolation.

Another possibility is to discretize your partial
differential equation in space by yourself and
use ODE13s to solve the resulting system of ordinary
differential equations (method of lines).

Best wishes
Torsten.
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