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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









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