Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Infinite expression, NDSolve
Replies: 1   Last Post: Oct 16, 2012 10:49 PM

 Messages: [ Previous | Next ]
 Kevin J. McCann Posts: 147 Registered: 12/7/04
Re: Infinite expression, NDSolve
Posted: Oct 16, 2012 10:49 PM

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!
>

Date Subject Author
10/16/12 grasley@gmail.com
10/16/12 Kevin J. McCann