Odd behaviour of solution of PDE

*To*: mathgroup at smc.vnet.net*Subject*: [mg116597] Odd behaviour of solution of PDE*From*: Alan Ford <fabio.sattin at igi.cnr.it>*Date*: Mon, 21 Feb 2011 05:34:21 -0500 (EST)

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

**Follow-Ups**:**Re: Odd behaviour of solution of PDE***From:*Oliver Ruebenkoenig <ruebenko@wolfram.com>