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

**References**:**Odd behaviour of solution of PDE***From:*Alan Ford <fabio.sattin@igi.cnr.it>