Re: [boost] Re: Numerical Integration - continued

From: Victor A. Wagner, Jr. (vawjr_at_[hidden])
Date: 2002-10-23 04:34:40

At Wednesday 2002/10/23 01:16, Martin Weiser <weiser_at_[hidden]> wrote:
>On Dienstag, 22. Oktober 2002 18:14, Victor A. Wagner, Jr. wrote:
> > At Tuesday 2002/10/22 08:31, Martin Weiser <weiser_at_[hidden]> wrote:
> > [deleted]
> >
> > >Huh? What's the integral over (3.5,6.78,5.89,2.0) then? I figure you
> > > mean summation instead of integration in this case, but I think this
> > > task is sufficiently different from integration to justify an
> > > interface of its own.
> >
> > This is exactly the kind of integration used in flight simulators where
> > the 'numbers' are coming from external inputs (e.g. the pilot).
> > Summation would be equivalent to "rectangular integration".  There are
> > other models which may work better.
>
>At least you need the integration points at which the values are given. It
>seems as if here an equidistant distribution is implicitly assumed, and
>the mesh size seems to be known implicitly as well...
>
>For my taste, these are too many implicit assumptions for a generally
>applicable library interface. In special applications, however, such a
>taylored interface may be perfectly appropriate.
>
> > Though in the simulations we used
> > to run, we _needed_ a signature something like:
> >
> > double integrate_step<method>(double next_delta_x, double
> > next_delta_t);
> >
> > Where often, delta_t would be a constant over the "run".  Other times,
> > it varied.
>
>It seems as if given only dx and dt, the only possibility to implement
>such a function is the explicit Euler scheme, i.e. rectangular
>integration - unless you store computed points and perform some multistep
>method. But I gather this would require an interface change.

I can't see why, method can include the information

>Now, with rectangular integration, we have the trivial implementation
>integrate_step(dx,dt) := dx*dt,

well, somewhat more to what we had...
integrate_step<rectangular>(dx, dt) would return   current_sum += dx*dt;

I may be misusing the terms here... we generally had  some  y = f'(t) and 
needed   f(t) given y and dt

>which hardly justifies an integration library. This, however, leads me to
>the thought I might have missed the point.
>
>Yours,
>Martin
>
>--
>Dr. Martin Weiser            Zuse Institute Berlin
>weiser_at_[hidden]                Scientific Computing
>http://www.zib.de/weiser     Numerical Analysis and Modelling
>
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Victor A. Wagner Jr.      http://rudbek.com
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