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Re: Memory and NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg85367] Re: Memory and NDSolve
• From: Oliver Ruebenkoenig <ruebenko at uni-freiburg.de>
• Date: Thu, 7 Feb 2008 06:32:50 -0500 (EST)
• References: <foek2h$i0m$1@smc.vnet.net>

Hi,

To integrate systems of differential algebraic equations or polynomial 
equations look at the IMTEK Mathematica Supplement:

http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/imsTOC/Differential%20Equation%20Systems/System%20Theory/TimeIntegrateDocu.html

or a BDF solver:
http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/imsTOC/Differential%20Equation%20Systems/System%20Theory/BDFDocu.html
(see example 4)

you might want to try a sub-space projection. this projects your original 
system of 1920 degrees of freedom to say 100 degrees of freedom, which of 
course are much faster to time integrate and use less memory.

http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/imsTOC/Differential%20Equation%20Systems/Model%20Order%20Reduction/ArnoldiDocu.html

hth,
Oliver

On Thu, 7 Feb 2008, PV wrote:

> Hello All,
> This is a general question that has reared up its head following my
> earlier question and discussion,
> (for the interested::
> http://groups.google.ca/group/comp.soft-sys.math.mathematica/browse_thread/thread/be4cfdb2c357400b?hl=en#b3d4099a15314475)
> I have a large matrix (1920*1920), simple first order differential
> equation that I try to solve using NDSolve. I need the value of the
> solution at just one point. The Interpolating Function object
> generated by NDSolve progressively becomes messier and larger crashing
> my code for the lack of memory.
> I have tried to free the memory occupied by the solution but that does
> not happen at all. Is there a better way to circumvent this problem?
> Cheers
> Prasanna
>
> PS: I remember Mr.Jens Kuska having replied to a similar post long ago
> with a Runge-Kutta integrator that evaluates the soln at just one
> point. I downloaded that but that does not seem to work with Matrix
> DEs since it may have been written for an older Mathematica version!
>
>

Oliver Ruebenkoenig, <ruebenko AT uni-freiburg.de>