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Re: NDSolve-memory

• To: mathgroup at smc.vnet.net
• Subject: [mg32040] Re: NDSolve-memory
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 20 Dec 2001 03:42:02 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <9vpnff$c9r$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

my package with Runge-Kutta solvers

http://phong.informatik.uni-leipzig.de/~kuska/visualsupp/RungeKuttaNDSolve.m

has a RKReturn option. With RKReturn->RKEndPoint no interpolation is
generated
and only the end point is returned. If you set RKReturn->
RKInterpolation an
interpolation function is generated.RKReturn->RKPoincareSection make a 
Poincare section on the hypersurface that is given by PSHyperplane
option.

The solvers expect a system of first order equations. The equations must
be 
autonom. The Runge-Kutta methods are for non-stiff and middle-stiff
problems.
With the Method option you can select methods of order 3-8 and atleast
the
higher order metthods should work with middle stiff problems.

The RKReturn->RKEndPoint option should solve your problem.

Regards
  Jens

Pieter-Jan.DeSmet at fys.kuleuven.ac.be wrote:
> 
> Dear readers,
> 
> I have a system of differential equations
> 
> F( y(t) ,y'(t) ,t )=0, with initial condition y(0) = y0.
> 
> Here y(t) is a vector-valued function, let us denote the dimension of
> this vector by n.  When I solve this system in Mathematica with NDSolve,
> the program uses too much memory and crashes if n is too big.
> (In my case this happens when n = 6).
> 
> I am however only interested in the value of y at t=1 ( y(1) ). So, I think
> that Mathematica can be more memory efficient if it throws away all
> previous values of y(t) it does not need anymore in its difference scheme. Is
> there a method to impose this? Of course, the result of NDSolve would not give
> an InterpolatingFunction object any more.
> 
> Other suggestions to reduce the needed memory are also appreciated. Lowering
> PrecisionGoal and AccuracyGoal does not seem have much effect on the memory.
> 
> Pieter-Jan De Smet