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MathGroup Archive 2007

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Re: Other PDE heat equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79740] Re: Other PDE heat equation
  • From: Miguel <misvrne at gmail.com>
  • Date: Fri, 3 Aug 2007 06:26:37 -0400 (EDT)
  • References: <f8pkd4$2vr$1@smc.vnet.net><f8s380$35j$1@smc.vnet.net>

On 2 ago, 10:05, Jens-Peer Kuska <ku... at informatik.uni-leipzig.de>
wrote:
> Hi,
>
> for you second order equation you have two drgrees of freedom in
> thr space direction, i.e., you can give (u[-L,t] and u[L,t]) or
> (u[-L,t] and D[u[x,t,x]/. x->L) or (D[u[x,t,x]/. x->-L and u[L,t])
> but you can't give three conditions, espcial not for inner points.
> In the inner points of the interval the differential equation rules and
> not any condition.
>
> But you can solve the equation on the interval x in [0,L] and use
> the symmetry of your equation (and the solution).
>
> Regards
>    Jens
>
>
>
> Miguel wrote:
> > How can I to resolve the unidirectional heat transmission for a plate
> > o slab:
>
> > a=0.03;hc=1890;k=34;L=0.03;
>
> > NDSolve[{a D[u[x,t],{x,2}]==D[u[x,t],t],
> > u[L,0]==600,  (* Initial value: the plate has the same temperature *)
> > u[-L,0]==600,
> > u[0,0]==600,
> > (D[u[x,t],x]/.x->0)==0  (* Max. in centre *)
> > (D[u[x,t],x]/.x->L)==(-hc/k)(u[L,t]-600)    (* Q convection = Q
> > conduction *)
> > u[L,t]==u[-L,t]},  (* Temper. symetric *)
> > u[x,t],{x,-L,L},{t,0,10}]
>
> > NDSolve::ivone: Boundary values may only be specified for one \
> > independent variable. Initial values may only be specified at one \
> > value of the other independent variable. >>
>
> > Where is my error?
>
> > Thanks- Ocultar texto de la cita -
>
> - Mostrar texto de la cita -

I have proved with all combinations of two boundaries conditions and I
obtain the same or similar error message

"NDSolve::bcedge: "Boundary condition ..."

In the other hand, I need all boundaries conditions to reslove
mannually. The main conditions are the simetry and the heat equality.



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