Re: Computational vs. analytical

From: Eric Gisse (fsegg_at_uaf.edu)
Date: 11/07/04 

Date: 6 Nov 2004 21:07:55 -0800

jimal1971@yahoo.co.uk (James J Albert) wrote in message news:<10715da5.0411060704.36870eba@posting.google.com>...
> Hi,
>
> I wonder if anyone on this group has heard
> of a debate regarding the impact of computers
> on physics. It seems that the overwhelming
> response is that computers have been a great
> benefit, but I know of at least one person
> who disagrees, saying that too many theoretical
> physicists now write software instead of
> pursuing analytical solutions and laws.
>
> Has there been a debate along these lines?

Yes and no.

The problem is that people who are making models sometimes extrapolate
outside the useful range of the model to the detriment of everyone. Im
looking at weather researchers here. Also, occasionally, people use
models in place of theory and experiment. I am looking at Henri Wilson
here.

The debate between numerical and analyitical as you form it does not
exist. The amount of stuff that is analytically unsolvable is much
much larger than the amount of stuff that is analyitically solvable.
There are things that need solutions but we can not explicitly solve
the way you would like. The 3-body problem is an example of that,
along with a whole host of differential equations [iterate through
linear, nonlinear, homogenous, nonhomogenous, partial, ordinary]

You can not analyitically solve x/h = tan(x), though the solutions of
x (called eigenvalues) which satisfy that equation are needed for
solving a particular form of the heat equation. The solutions TO that
equation are trivially obtainable through a numerical method called
"Newton's mathod".

>
> Any books/references?

Any modern numerical analysis book. Apply it to any math, physics or
engineering text with a decent set of nonlinear partial or ordinary
differential equations.

While looking at a modern numerical book, you might want to look up
Newton's method.

The numerical book im using at the moment is "Numerical Analysis and
Scientific Computation" by Leader. It was published just this year. It
is also tied intimately with MATLAB, which is a damn useful program.

>
> Thanks very much in advance.
>
> Jim.

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