Solving a PDE with fixed endpoints

*To*: mathgroup at smc.vnet.net*Subject*: [mg70756] Solving a PDE with fixed endpoints*From*: "Charlie Brummitt" <cbrummitt at wisc.edu>*Date*: Thu, 26 Oct 2006 02:38:58 -0400 (EDT)

Hello, I am trying to solve PDE's with fixed endpoints. That is, my function is u[x,t], and I fix u[0,t] = A and u[L,t]=B, where A and B are constants. However, when I solve these PDE's out to, say, time t = 8,000, I find that the endpoints don't always stay fixed. Instead, they sometimes "drift" away from A and B. An example is shown in the following JPG images: 3D plot of times 7000 through 8000 and plot of u at the final time. Note that the endpoints should be fixed at 0.1 on both ends, but the left end (u(0,t)) drifts downward to -120. http://i13.tinypic.com/2roqszm.jpg Here is the initial condition, showing that the endpoints should be fixed at 0.1 on both ends: http://i14.tinypic.com/4humgww.jpg Should I be circumspect of the solution that NDSolve gives me if the endpoint condition isn't satisfied correctly for all time? Is there any way I could fix this? I think this phenomenon of the end points drifting away from A, B occurs whenever there is a constant term in the equation. That is, du/dt = const. + (rest of equation). Thus, this constant term increases the value of u at every spatial point, which makes it hard (impossible?) to satisfy the endpoint conditions. Thanks for any ideas/suggestions you may have, Charlie