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Topic: System of 1D PDEs with coupled boundary conditions
Replies: 5   Last Post: Aug 23, 2013 5:26 AM

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Luminita T.

Posts: 3
Registered: 8/22/13
Re: System of 1D PDEs with coupled boundary conditions
Posted: Aug 22, 2013 11:04 AM
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"Torsten" wrote in message <kv589c$j2g$>...
> "Luminita T." wrote in message <kv56d9$k7n$>...
> > I've have a system of 4 parabolic PDE with boundary conditions that I would like to integrate in time starting from initial conditions.
> >
> > I've been trying to put the system into the pdepe() format, but it seems that I can't give coupled boundary conditions, in particular something of the form: a*DuDx(1) + b*DuDx(2) + c*DuDx(3) = 0.
> >
> > As far as I could see from the help, q(x,t) needs to be specified as a vector-valued function that is element-wise multiplied with f(x,t,u,DuDx), which in my case is just DuDx. This does not allow to express linear combinations of elements of f() for a boundary condition.
> >
> > If q(x,t) could be a matrix-valued function, then it could be done.
> > Is it possible to somehow specify coupled boundary conditions in pdepe() ?
> >
> > Alternatively, I've been looking at the pdetool() for 2D spatial PDE. It seems a bit more complicated to handle and I'll have to put a bit of time into it. At this point, I can't say directly from the UserGuide (2. Setting up your PDE >>Types of Boundary Conditions) if it can handle the coupled boundary conditions. Any help figuring this out is much appreciated.
> >

> Usually, the boundary condition for equation i refers directly to the flux defined in equation.
> Thus if f for equation i is given as
> f(i)=a*du1/dx + b*du2/dx + c*du3/dx,
> you simply have to put
> p(i)=0 and q(i)=1
> to define the boundary condition
> a*du1/dx + b*du2/dx + c*du3/dx = 0.
> Best wishes
> Torsten.

Hmm, my normal flux functions are f(1) = a1*du1/dx; f(2) = a2*du2/dx, etc. Separate terms. But then maybe I can introduce a "fake" or "helper" equation to have this new flux to use in the boundary condition.

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