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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.
regards
--
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 http://bioinformatics.cat.nyu.edu
"Hello New York! We'll do what we can!"
Bill Murray in `Ghostbusters'.
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- Re: Help with ODE solver, (continued)
- Re: Help with ODE solver, John W. Eaton, 2002/09/12
- Re: Help with ODE solver, Marco Antoniotti, 2002/09/12
- Message not available
- Re: Help with ODE solver, John W. Eaton, 2002/09/12
- Re: Help with ODE solver, Marco Antoniotti, 2002/09/12
- Re: Help with ODE solver, John W. Eaton, 2002/09/12
- Re: Help with ODE solver, Marco Antoniotti, 2002/09/12
- Re: Help with ODE solver, John W. Eaton, 2002/09/12
- Re: Help with ODE solver, Marco Antoniotti, 2002/09/13
- Re: Help with ODE solver, John W. Eaton, 2002/09/13
- Re: Help with ODE solver, Jon Davis, 2002/09/13
- Re: Help with ODE solver,
Marco Antoniotti <=
- Re: Help with ODE solver, Martin Senator, 2002/09/12