NDSolve -- limitations and a product suggestion
- To: mathgroup at smc.vnet.net
- Subject: [mg67587] NDSolve -- limitations and a product suggestion
- From: "Alan" <info at optioncity.REMOVETHIS.net>
- Date: Sat, 1 Jul 2006 05:12:30 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I am very impressed with NDSolve for PDEs and am using it more and more. However, as the documentation says, "The boundary conditions can be a linear combination of Dirichlet and Neumann type conditions and can be time dependent." The thing is, for parabolic problems often the -correct- mathematics is that no boundary conditions are needed at an endpoint. The solver will accept boundary conditions when none are allowed (without a warning), producing what may be an incorrect solution, and warn if you leave them out, but sometimes producing a correct solution. This is dangerous. My product suggestion: add special options for NDSolve specifically for parabolic problems with one spatial dimension with one or two singular boundaries. Have the user specify the nature of each boundary. These are completely classified from the underlying diffusion: regular, exit, entrance, natural. For example, if the user says a boundary is natural, then the program invokes a built-in method for that and won't accept a boundary condition there. This would both improve the mathematical correctness of the product and be very useful. Thanks for listening! alan