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Re: Help with ODE solver

From: Marco Antoniotti
Subject: Re: Help with ODE solver
Date: Fri, 13 Sep 2002 11:42:13 -0400

> Date: Fri, 13 Sep 2002 11:19:00 -0400 (EDT)
> From: Jon Davis <address@hidden>
> cc: Marco Antoniotti <address@hidden>, <address@hidden>
>       I hate to throw spanners into projects, but there are
> serious technical issues with "solving" differential equations
> with discontinuous  right hand sides. In particular, the standard
> existence and uniqueness theorems are inoperable, and even the
> definition of "solution" is subtle.
>       The classical reference is a paper by Fillipov that
> appears in the AMS Translations Series, Volume ?? Solutions need
> not be unique in the usually understood sense, and even if an
> algorithm computes a trajectory that is a Fillipov solution, you
> need not see that in a physical apparatus. Generally such problems
> raise modelling issues, and questions about whether the physical model
> is really discontinuous, or exquisitely sensitive to structure
> assumptions.

Look.  I know that there are problems.

However.  I have a system that I have to study in the presence of
external "stimuli".  So, either I can simply say

  "from time t_i the variable X (a constant) will have a value K"

or I have to model the system as a non-discontinuous system with a
very sharp step function for the variable X.

I'd appreciate any help about how to go ahead and model this second
case in Octave/Matlab.

Please understand that it is not out of lazyness that I am asking
this.  I just figured that other people may have had this problem
before and that I could reuse some experience.


Marco Antoniotti ========================================================
NYU Courant Bioinformatics Group        tel. +1 - 212 - 998 3488
715 Broadway 10th Floor                 fax  +1 - 212 - 995 4122
New York, NY 10003, USA       
                    "Hello New York! We'll do what we can!"
                           Bill Murray in `Ghostbusters'.

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