Automatic Time Step for an ODE

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3 total messages Started by engrand Thu, 05 Nov 1992 11:05

#673

Author: engrand
Date: Thu, 05 Nov 1992 11:05

26 lines
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Hi there,
I just got the news here, so I don't if I can post, and, if I can, whether my question
has already been asked.

Anyway,

I'm studying different methods to automatically change the size of a time step
when solving a time-dependant ODE. Automatically means that the code should
know when it has to use a larger or smaller time step, 
according to what happens to the sytem. 

I'm interested in this problem for a general ODE first. I'd like to see
all that can be done , to be able to choose, then, which method is the most adapted
to my specific problem which is a stiff ODE.
Actually, it's a parabolic PDE (neutronic diffusion equations) on which
we apply finite volumes (or finite differences) to end up
with a time dependant system of ODE.


I'm interested in getting some references in the litterature.
I haven't heard on any book dealing with this problem (but I haven't looked
very hard) ; is there any ?

Thanks in advamce for answering,
Phil.

Re: Automatic Time Step for an ODE

#679

Author: Mike Hosea
Date: Thu, 05 Nov 1992 19:32

25 lines
1769 bytes

In article <1992Nov5.110534.15386@edf.fr> engrand@clt13vf.der.edf.fr writes:
>
>I'm studying different methods to automatically change the size of a time step
>when solving a time-dependant ODE. Automatically means that the code should
>know when it has to use a larger or smaller time step, 
>according to what happens to the sytem. 
>
>I haven't heard on any book dealing with this problem (but I haven't looked
>very hard) ; is there any ?

All modern mathematical software for solving general ODE initial value problems 
control the step size automatically, though some require that you supply the
initial step size.  I don't know of any books written solely on this subject,
but you may wish to consult the relevant sections of

_Solving_Ordinary_Differential_Equations_I_, by Hairer, Norsett, and Wanner

_Solving_Ordinary_Differential_Equations_II_, by Hairer, and Wanner.

The first volume addresses nonstiff problems and the second stiff problems.
There should be enough references in those texts to get you started in the
literature.
-- 
Regards,
Mike Hosea (mhosea@seas.smu.edu)

Re: Automatic Time Step for an ODE

#701

Author: Kjell Gustafsson
Date: Fri, 06 Nov 1992 12:01

36 lines
2209 bytes

In article <1992Nov5.110534.15386@edf.fr> engrand@clt13vf.der.edf.fr writes:
>
>I'm studying different methods to automatically change the size of a time step
>when solving a time-dependant ODE. Automatically means that the code should
>know when it has to use a larger or smaller time step, 
>according to what happens to the sytem. 
>
>I haven't heard on any book dealing with this problem (but I haven't looked
>very hard) ; is there any ?

I've studied this problem in my thesis "Control of Error and
Convergence in ODE Solvers", Kjell Gustafsson, Department of Automatic
Control, Lund Institute of Technology, Sweden, 1992". It turns out
that with some ideas from feedback control you can get a better
understanding of the stepsize adjustment problem and also design
improved algorithms. 

Part of the material (the one concerning explicit methods) is
published in ACM TOMS: "Control Theoretic Techniques for Stepsize
Selection in Explicit Runge-Kutta Methods", Kjell Gustafsson, 17:4,
1991, pp. 533-554.

Kjell

-------------------------------------------------------------------------------
    mail: Kjell Gustafsson, Department of Computer Science MJH309
          Stanford University, Stanford CA 94305, USA
  e-mail: kjell@sccm.stanford.edu
   phone: (415) 723-4269 (voice), (415) 723-2411 (fax)

--
-------------------------------------------------------------------------------
    mail: Kjell Gustafsson, Department of Computer Science MJH309
          Stanford University, Stanford CA 94305, USA
  e-mail: kjell@sccm.stanford.edu
   phone: (415) 723-4269 (voice), (415) 723-2411 (fax)

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