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Help me : Solve a simple PDE in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110492] Help me : Solve a simple PDE in Mathematica
  • From: thaihang le <thaihang.le at gmail.com>
  • Date: Mon, 21 Jun 2010 02:10:35 -0400 (EDT)

Dear all,

I have a PDE in cylindrical coordinate but i cant imply the boundary
condition :
In the text book, i have this equation :

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).

I cant find the solution ....

==================================================================================

In fact, i want to find the solution of this problem, using NDSolve.
The problem is stated in this demonstration :
http://demonstrations.wolfram.com/ScanningElectrochemicalMicroscopyDiffusionOnAMicrodiskElectr/


Thanks for your help !


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