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delayed (numerical) matrix inversion in NDSolve?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131625] delayed (numerical) matrix inversion in NDSolve?
  • From: "vadim.oganesyan at gmail.com" <vadim.oganesyan at gmail.com>
  • Date: Fri, 13 Sep 2013 00:35:15 -0400 (EDT)
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Hi,

How do I get NDSolve to solve coupled ODE system in the form

P[v].v'==Q[v]?

P[v] and Q[v] contain all kinds of trig functions etc. but I am more or less guaranteed the existence of nice smooth solutions v, as well as 1/P for the problem at hand.

As far as I can tell the difficulty is in the way NDSolve prepares the equations before iterating (using Solve, apparently?!?!): for small sizes <=4 NDSolve works without a hitch but for larger ones it hangs up.  

I have tried asking it to solve v'==(P)^(-1)Q and use delayed inverse to try and force numerical evaluation of the right-hand-side (which is easy) but no luck.

I gave up and hand-coded a simple RK4 and/or Euler and it worked without a hitch, so I am pretty sure the problem is in the NDSolve being stubborn on the initial step.

thoughts? thanks,v



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