       Re: Numerical solution of the heat equation on a disk with Dirichlet

• To: mathgroup at smc.vnet.net
• Subject: [mg113637] Re: Numerical solution of the heat equation on a disk with Dirichlet
• From: schochet123 <schochet123 at gmail.com>
• Date: Fri, 5 Nov 2010 05:13:52 -0500 (EST)
• References: <iatsr4\$eco\$1@smc.vnet.net>

```Try replacing 1/r by 1/(r+10^(-50)).

For example,

NDSolve[{D[u[t, r], t] ==
D[u[t, r], r, r] +
D[u[t, r], r]/(r + 10^(-50)), (D[u[t, r], r] /. r -> 0) == 0,
u[0, r] == Cos[Pi r/2], u[t, 1] == 0}, u, {r, 0, 1}, {t, 0, 1}]

Steve

On Nov 4, 11:02 am, Francois Fayard <FFay... at slb.com> wrote:
> Hello,
>
> I would like to get a numerical simulation of the heat equation with Dirichlet boundary conditions on a disk. With the problem I have, the function does not depend on theta, so we get :
>
> u_t = u_rr + (1/r) u_r
>
> It introduces a singularity as goes to 0 and Mathematica can not solve the problem with NDSolve. Is there a way to go around this ?
>
> Best regards,
> Francois
>
> PS : I know that I can do Bessel expansion, but it's not what I want to do here.

```

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