       Re: Odd behaviour of solution of PDE

• To: mathgroup at smc.vnet.net
• Subject: [mg116605] Re: Odd behaviour of solution of PDE
• From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
• Date: Mon, 21 Feb 2011 06:18:44 -0500 (EST)
• References: <201102211034.FAA22078@smc.vnet.net>

```

On Mon, 21 Feb 2011, Alan Ford wrote:

> Dear all,
>
> I encountered an odd behaviour with this PDE:
>
> dy/dt = d(D(x) dy/dx - U(x) y) + S(x,t)
>
> It is a standard diffusion-convection equation with time-and space-
> dependent source term.
> I wrote it in cartesian coordinate, but actually in my problem it is
> written in cylindrical coordinates,
> thus x is the radius:   eps < x < 1.  eps is a very small number, set
> different to zero to avoid trouble
> with the singular point at the origin.
>
> The PDE is supplemented with initial condition y = 0 at t = 0, and two
> boundary conditions:
> one is dy/dx = 0 at x = eps, and the other is a time-dependent BC at x
> = 1, y(x=1) = y_BC(t).
>
>
> The odd thing is this: I ask Mathematica (v. 7) to solve for y between
> eps < x < x0
> with x0 < 1, NO MATTER how smaller than unity (say, x0 = 0.999).
> Everything works
> apparently fine, i.e, the solution reaches asymptotically a stable
> state.
> Now, I set the outer bound of integration to 1, i.e, place it at the
> location where the boundary condition
> is fixed. Then, the solution diverges in time.
> Notice that there nothing special in 1, and I made checks with other
> values: whenever I
> set x0 = x_BC, the solution looks wrong. On the other hand, as soon as
> I make
> the difference x_0 - x_BC as small as I wish (but non-zero, say
> 10^(-5)), then everything is OK.
>
> Anybody has guesses about why this strange behaviour ?
>
>
> Thanks for any help
>
> Fabio
>
>
>
>

Fabio,

this is difficult to say without seeing the actually code. Could you send
it?

Oliver

```

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