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Solving very large systems of ODEs with NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg115331] Solving very large systems of ODEs with NDSolve
• From: Gabriel Landi <gtlandi at gmail.com>
• Date: Fri, 7 Jan 2011 04:13:58 -0500 (EST)

Greetings all.

The problem I have in my hands is to solve a very large (500 to 10 000 or +)
system of non-linear dense ODEs (the Landau-Lifshitz equations in
particular).

In general, I think what I perhaps would like to ask is general advice on
implementing large systems in the NDSolve Framework
In particular, some of the problems that arose are:

 - In certain cases, I am not interested in storing the solution to all the
variables for all t. All I need is the value of each dependent variable at
the final integration time. I have been using combos of DependentVariables
and the EventLocator method but so far I haven't been able to formulate the
problem in a efficient way.

 - Each equation has a invariant and using the projection method to control
the error on these invariants turned out to be a very nice thing.
Unfortunately, if the system gets larger than 100 or so equations, the
kernel immediately crashes when I call this method (with no message at all).
I am not sure why since, when memory is the problem, a message is issued.
Anyone have any thoughts on this?

Thanks in advance for any suggestions,

Cheers,

Gabriel Landi