Re: Differential eqation: command set up
- To: mathgroup at smc.vnet.net
- Subject: [mg79598] Re: Differential eqation: command set up
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Tue, 31 Jul 2007 06:01:16 -0400 (EDT)
- Organization: Uni Leipzig
- References: <f8kg2j$2i6$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
Hi,
a) your boundary/initial conditions are inconsistent and so no
solution exist
b)
With[{A = 1},
sol = NDSolve[
{
D[u[x, t], t] == A*D[u[x, t], {x, 2}],
u[-1, t] == 1, u[1, t] == 1,
u[x, 0] == Exp[-(Abs[x] - 1)^2/2]^64
}, u[x, t], {x, -1, 1}, {t, 0, 1}]
]
Plot3D[
u[x, t] /. sol[[1]], {x, -1, 1}, {t, 0, 1}, PlotRange -> All]
uses a consistent initial condition.
Regards
Jens
Elias wrote:
> I want to solve the following differential equation through Mathematica:
>
> du/dt=A*(d^2)u/dx^2 , A=const
>
> Practically, this is the diffusion equation.
>
> The boundary + initial conditions I have are:
>
> * u(t=0, -1<x<1) =0
> * u(t=0, x>=1, x<=-1) =1
>
> I cant find the way to input these initial/boundary conditions in a command.
>
> Any ideas?
>
> Thanks in advance!
>