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From: Fränzis21 Petzold on 9 Aug 2010 11:35
Hello,
I´m trying to solve a system of partial differential and ordinary differential equations.
The system of equations is described by the following two equations:

du1/dt=A*du2/dx

du2/dx=B*(u1-u2)

u1 is only dependent on the time t; u2 is dependent on the two variables time t and position x. It follows that u1 is an ordinary differential equations and u2 is a partial differential.
So my question is now, how can I solve this system of equations in matlab?

I am very grateful for any help.
From: Torsten Hennig on 9 Aug 2010 22:51
> Hello,
> I´m trying to solve a system of partial differential
> and ordinary differential equations.
> The system of equations is described by the following
> two equations:
>
> du1/dt=A*du2/dx
>
> du2/dx=B*(u1-u2)
>
> u1 is only dependent on the time t; u2 is dependent
> on the two variables time t and position x. It
> follows that u1 is an ordinary differential equations
> and u2 is a partial differential.
> So my question is now, how can I solve this system of
> equations in matlab?
>
> I am very grateful for any help.


What do you know about u2 at the endpoints of the
x-interval of integration ?

Best wishes
Torsten.
From: Franz Petzold on 10 Aug 2010 07:25
Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <1155730886.85180.1281423099648.JavaMail.root(a)gallium.mathforum.org>...
> > Hello,
> > I´m trying to solve a system of partial differential
> > and ordinary differential equations.
> > The system of equations is described by the following
> > two equations:
> >
> > du1/dt=A*du2/dx
> >
> > du2/dx=B*(u1-u2)
> >
> > u1 is only dependent on the time t; u2 is dependent
> > on the two variables time t and position x. It
> > follows that u1 is an ordinary differential equations
> > and u2 is a partial differential.
> > So my question is now, how can I solve this system of
> > equations in matlab?
> >
> > I am very grateful for any help.
>
>
> What do you know about u2 at the endpoints of the
> x-interval of integration ?
>
> Best wishes
> Torsten.

Thank you for your answer.
This systems of equations is representing the model of a short regenerator, which is a special form of a heat exchanger. u1 stands for the temperature of the storage mass, therefor it can be just called T_S. This temperature is only depend on time and independent of the position x in the storage mass. u2 describes the temperature of the gas, for example air.
I only know that the temperature of the gas at the endpoint of the x-interval is the endtemperature of the gas.
I´ve already solved this system of equations in an analytic way, my only problem is, how to solve it in matlab to visualize the solution.
From: Torsten Hennig on 10 Aug 2010 03:59
> Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote
> in message
> <1155730886.85180.1281423099648.JavaMail.root(a)gallium.
> mathforum.org>...
> > > Hello,
> > > I´m trying to solve a system of partial
> differential
> > > and ordinary differential equations.
> > > The system of equations is described by the
> following
> > > two equations:
> > >
> > > du1/dt=A*du2/dx
> > >
> > > du2/dx=B*(u1-u2)
> > >
> > > u1 is only dependent on the time t; u2 is
> dependent
> > > on the two variables time t and position x. It
> > > follows that u1 is an ordinary differential
> equations
> > > and u2 is a partial differential.
> > > So my question is now, how can I solve this
> system of
> > > equations in matlab?
> > >
> > > I am very grateful for any help.
> >
> >
> > What do you know about u2 at the endpoints of the
> > x-interval of integration ?
> >
> > Best wishes
> > Torsten.
>
> Thank you for your answer.
> This systems of equations is representing the model
> of a short regenerator, which is a special form of a
> heat exchanger. u1 stands for the temperature of the
> storage mass, therefor it can be just called T_S.
> This temperature is only depend on time and
> independent of the position x in the storage mass. u2
> describes the temperature of the gas, for example
> air.
> I only know that the temperature of the gas at the
> endpoint of the x-interval is the endtemperature of
> the gas.
> I´ve already solved this system of equations in an
> analytic way, my only problem is, how to solve it in
> matlab to visualize the solution.

You say u2 depends in position x - thus du2/dx
depends on position x.
Now if u1 which is given by
du1/dt = A*du2/dx (1)
does _not_ depend on position, du2/dx in (1) must be
evaluated at a _fixed_ position.
Is this correct ?

Further:
To solve
du2/dx = B*(u1-u2)
for u2, u2 must be given at one of the endpoints
of the x-interval.
Do you have its value there ?

Best wishes
Torsten.
From: Franz Petzold on 13 Aug 2010 06:36
Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <489511086.86400.1281441570363.JavaMail.root(a)gallium.mathforum.org>...
> > Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote
> > in message
> > <1155730886.85180.1281423099648.JavaMail.root(a)gallium.
> > mathforum.org>...
> > > > Hello,
> > > > I´m trying to solve a system of partial
> > differential
> > > > and ordinary differential equations.
> > > > The system of equations is described by the
> > following
> > > > two equations:
> > > >
> > > > du1/dt=A*du2/dx
> > > >
> > > > du2/dx=B*(u1-u2)
> > > >
> > > > u1 is only dependent on the time t; u2 is
> > dependent
> > > > on the two variables time t and position x. It
> > > > follows that u1 is an ordinary differential
> > equations
> > > > and u2 is a partial differential.
> > > > So my question is now, how can I solve this
> > system of
> > > > equations in matlab?
> > > >
> > > > I am very grateful for any help.
> > >
> > >
> > > What do you know about u2 at the endpoints of the
> > > x-interval of integration ?
> > >
> > > Best wishes
> > > Torsten.
> >
> > Thank you for your answer.
> > This systems of equations is representing the model
> > of a short regenerator, which is a special form of a
> > heat exchanger. u1 stands for the temperature of the
> > storage mass, therefor it can be just called T_S.
> > This temperature is only depend on time and
> > independent of the position x in the storage mass. u2
> > describes the temperature of the gas, for example
> > air.
> > I only know that the temperature of the gas at the
> > endpoint of the x-interval is the endtemperature of
> > the gas.
> > I´ve already solved this system of equations in an
> > analytic way, my only problem is, how to solve it in
> > matlab to visualize the solution.
>
> You say u2 depends in position x - thus du2/dx
> depends on position x.
> Now if u1 which is given by
> du1/dt = A*du2/dx (1)
> does _not_ depend on position, du2/dx in (1) must be
> evaluated at a _fixed_ position.
> Is this correct ?
>
> Further:
> To solve
> du2/dx = B*(u1-u2)
> for u2, u2 must be given at one of the endpoints
> of the x-interval.
> Do you have its value there ?
>
> Best wishes
> Torsten.


Hello Torsten,
thank you for your messages. But I´ve solved this problem in an another way.
Thanks anyway.
Best wishes
Franz
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