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Re: Help me : Solve a simple PDE in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110505] Re: Help me : Solve a simple PDE in Mathematica
  • From: schochet123 <schochet123 at gmail.com>
  • Date: Mon, 21 Jun 2010 04:55:19 -0400 (EDT)
  • References: <hvmvoo$pp1$1@smc.vnet.net>

The reason for the message about a condition
"not specified on single edge" is  that
the boundary condition b2 is not given on
an edge of the domain. The fact that
condition b3 is mentioned in the error message
instead of b2 seems to be a  bug in the error handling code.

However, if you change the domain to {r,10^{-5),1} you will discover
the sad fact that NDSolve does not handle pure multidimensional boundary
value problems, only initial boundary value problems. You will therefore
have to code it yourself or look for a person or a Package that has
already done so. Note that the demonstration you cite uses an exact formula
from some book, although they claim, without providing code that NDSolve
obtains their solution, which is hard to tell since their boundary conditions
seem either garbled or incomplete.

Steve

On Jun 21, 9:10 am, thaihang le <thaihang... at gmail.com> wrote:
>
> eqn = D[u[r,z],{z,2}]+D[u[r,z],{r,2}+D[u[r,z],{r,1}]*1/r == 0
>
> b1 = ( D[u[r,z],{z,1}]/.z->0 ) ==0
> b2 = ( D[u[r,z],{r,1}]/.r->10^-5 ) ==0
> b3= u[r,2]==1
> b4 =u[2,z] ==1
>
> NDSolve[{eqn,b1,b2,b3,b4},u,{r,0,2},{z,0,2}] ==> Error : u[2,z]===
1 is
> not specified on single edge
>
> and i dont use b4 :
> NDSolve[{eqn,b1,b2,b3},u,{r,0,2},{z,0,2}] ===> Error : Number of
> constraint (1) is not equal total diff (2).
>


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