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Re: Odd behaviour of solution of PDE

• To: mathgroup at smc.vnet.net
• Subject: [mg116608] Re: Odd behaviour of solution of PDE
• From: Alan Ford <fabio.sattin at igi.cnr.it>
• Date: Mon, 21 Feb 2011 19:28:39 -0500 (EST)
• References: <201102211034.FAA22078@smc.vnet.net> <ijthmr$mn1$1@smc.vnet.net>

Hi Oliver,

I had sent an answer to your question, providing
a simple piece of code, but it seems the post was lost.

So, rather than submitting the whole matter again,
I would rather formulate my question as a more general issue.

Suppose you want to integrate a PDE in time and in space,
the range being a <= x <= b.
You have to set boundary conditions.
By mistake, you set one boundary condition not at x = b (the extremum
of integration)
but at x = b + eps (i.e, beyond it).
Mathematica does not complain about it and returns a solution.
My guess was that Mathematica did integrate from x = a to x = b + eps,
in order to match
boundary condition, and then returned solution only in the range
(a,b).
So, no harm, after all.
However, it does not look like the case: in all cases I could
benchmark mathematica
result versus independent solutions, Mathematica simply computes a
wrong solution.
namely, at the first time step it jumps from the initial condition to
a completely wrong value,
and then relaxes with a trend quite similar to the correct one.

At this time, I'm not asking for hints: it is now quite clear that,
contrary to my belief
in the first post, mathematica is definitely not providing a correct
answer when I supply
the "wrong" boundaries.
But I am wondering why mathematica does not acknowledge that it is
doing an illegal operation

Fabio

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