Date: Aug 22, 2013 10:47 AM
Author: Torsten
Subject: Re: System of 1D PDEs with coupled boundary conditions

"Luminita T." wrote in message <kv56d9$k7n$1@newscl01ah.mathworks.com>...
> 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.