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Re: NDSolve is using Solve?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131624] Re: NDSolve is using Solve?
  • From: "vadim.oganesyan at gmail.com" <vadim.oganesyan at gmail.com>
  • Date: Fri, 13 Sep 2013 00:34:55 -0400 (EDT)
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  • References: <ilabut$1tq$1@smc.vnet.net>

On Thursday, March 10, 2011 6:16:45 AM UTC-5, Oliver Ruebenkoenig wrote:
> On Wed, 9 Mar 2011, J.Frazer wrote:
>
> > Hello everyone,
> >
> > This is my first time posting so my apologies if I'm going about this
> > the wrong way. I'm having the following problem:
> >
> > I'm using NDSolve but its not managing to get to the solution even if I
> > leave it running over the weekend. If I greatly simplify one of the
> > equations I can get a result but in either case I get the error messages
> >
> > Solve:: incnst
> > Solve:: ifun
> >
> > This worries me as if its trying to simplify analytically, presumably as
> > the equations becomes more complicated this will become incredibly time
> > consuming.
> >
> > Do people agree this may be the cause of the long running time? If so,
> > is there a way of stopping NDSolve from using Solve?
> >
> > Cheers,
> >
> > Jonny
> >
> >
> Hi Jonny,
>
> yes NDSolve uses Solve internally but that is only for pre processing
> purposes. If this is really the cause for the slow NDSolve (maybe it is a
> hard problem...)  It were best if you could send some working code, then
> we could have a look at it and see if anything can be done.
>
> Oliver

Hi,

I have encountered a similar problem, I think:

I have re-parametrized a relatively simple system of linear ODEs

u'=L.u

into something more complicated looking

M[v].v'=N[v],

but it really is the same problem with new coordinates, so the solution must exist (except near a few possible singularity points of the coordinate change)

feeding this or v'=Inverse[M[v]].N[v] into NDSolve has ONLY worked for small enough problems where the inverse can be done analytically. Otherwise, it spends forever in the prep stage for the calculation.

I have played around with defining a delayed Inverse etc but nothing worked, so I gave up and coded up a simple RK4 routine and forgot about it, but now I am returning to this problem and would like to get Mathematica to work, which I think it should be able to.

Thoughts?
Thanks,Vadim



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