Re: Infinite expression, NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg128406] Re: Infinite expression, NDSolve*From*: "Kevin J. McCann" <kjm at KevinMcCann.com>*Date*: Tue, 16 Oct 2012 20:11:30 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <k5j254$8r3$1@smc.vnet.net>

Your problem is twofold, I think. One is the obvious numerical singularity at r=0. Here you could try using r=0.00001 or some such to get around it, but care must be taken. The second problem is the inconsistency of the boundary conditions T[1,t]= and T[r,0]==0. Kevin On 10/16/2012 3:25 AM, Grasley wrote: > Dear All, > > I am trying to use NDSolve to solve the heat equation for 1-D radial flow in cylindrical coordinates, with the initial condition of a spatially constant temperature, and boundary conditions of zero flux at r=0 (axisymmetry) and a constant temperature at a radius of 1. Here is the code: > > NDSolve[{D[T[r, t], t] == 1/r*D[r D[T[r, t], r], r], > Derivative[1, 0][T][0, t] == 0, T[1, t] == 20, T[r, 0] == 0}, T, {r, > 0, 1}, {t, 0, 10}] > > Power::infy: Infinite expression 1/0. encountered. >> > > Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >> > > Power::infy: Infinite expression 1/0. encountered. >> > > Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >> > > NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0.`. >> > > I've tried using nonzero (i.e. very small values) for the initial time and in place of r=0 in the boundary condition, but to no avail. Any ideas? > > Thanks! >