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). >> > >