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