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.