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Re: NDSolve profiling

• To: mathgroup at smc.vnet.net
• Subject: [mg126979] Re: NDSolve profiling
• From: Narasimham <mathma18 at hotmail.com>
• Date: Thu, 21 Jun 2012 05:21:15 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jrrvgu$4sd$1@smc.vnet.net>

On Jun 20, 12:53 pm, Ben <Benjamin.R.Le... at gmail.com> wrote:
> Are there any tricks to profiling/optimising NDSolve?
>
> A computationally expensive subexpression (involving ProductLog) is repea=
ted many times in my ODE, so I'd like to check whether it is only computed =
once per evaluation point (and would also like to try other possible optimi=
sations like using compile unless that is already redundant).
>
> My ODE has multiple coupled-components so I've also experimented with con=
verting it into vector form. With simpler ODEs I've found this has facilita=
ted using compiled functions in NDSolve (and gave an overall speed boost), =
but with my current ODE I find that the vector form causes failure. I'm won=
dering whether switching from a coupled set of equations to vector form of =
the identical ODE/IVP may cause the algorithm pick a different step sequenc=
es, or may be more likely to produce catastrophic-cancellation inaccuracies=
?
>
> Can anybody share relevant insight into the evaluation that goes on behin=
d the scenes of ndsolve's equation-processing and iteration, and how to deb=
ug or ways to optimise it for speed?
>
> Thanks,
> Ben

If the relations are explicitly and logically defined there may be no
problems.Sometimes what appears as a narrow deviation may be
surprising; but in any case at least a representative code should be
posted here to help avoid vagueness,to pinpoint the problem.

Narasimham