Re: [boost] Re: Numerical Integration - continued

From: Martin Weiser (weiser_at_[hidden])
Date: 2002-10-23 03:16:33

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.

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