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Re: Help me : Solve a simple PDE in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110507] Re: Help me : Solve a simple PDE in Mathematica
  • From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
  • Date: Tue, 22 Jun 2010 06:59:28 -0400 (EDT)

Hi,

On Mon, 21 Jun 2010, schochet123 wrote:

> 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

http://library.wolfram.com/infocenter/Conferences/7549/

Perhaps this helps,

Oliver

> 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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