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In article <26AUG199218380252@robin.rp.csiro.au>
awhichel@robin.rp.csiro.au (Adrian Whichello) writes:
>	I just read in Numerical Recipes that predictor-corrector methods for
>solving initial value ODE's are dead, or at least on their way out. This
>strikes me as rather strong, but I would like some other opinions. What do you
>think? 

Numerical Recipes is (very) wrong here.  Predictor-Corrector (PC)
methods for non-stiff initial value ODE integration are alive and
well.  ODE experts (which I'm not) recommend them as being robust
and efficient for a wide range of problems.  See, for example, the
review and discussion in:
\mybibitem{Gear, C. W.}{1981}
        ``Numerical Solution of Ordinary Differential Equations:
          Is There Anything Left to Do?''
        SIAM Review {\bf 23}(1), 10--24.

Indeed, of the current high quality "black box" ODE codes, a large
fraction use PC methods.  Notable examples include Hindmarsh's LSODE
suite, and the Shampine & Gordon DE/STEP package.

PC methods are also "culturally similar" to the backwards
differentiation multistep methods which seem to be the current
favorites for stiff ODEs, which makes it easier to combine both in
a single general purpose code or code suite.  (For example, LSODE
does this.)

- Jonathan Thornburg
  <jonathan@einstein.ph.utexas.edu> or <jonathan@hermes.chpc.utexas.edu>
  University of Texas at Austin / Physics Dept / Center for Relativity
  and (for a few more months) U of British Columbia / {Astronomy,Physics}

In article <26AUG199218380252@robin.rp.csiro.au>, awhichel@robin.rp.csiro.au (Adrian Whichello) writes:
> Dear Netters
> 
> 	I just read in Numerical Recipes that predictor-corrector methods for
> solving initial value ODE's are dead, or at least on their way out. This
> strikes me as rather strong, but I would like some other opinions. What do you
> think? 
> 					Adrian P. Whichello

Whilst NR provides a broad coverage, there is much in NR which is at fault
in both the text and the software from the standpoint of modern numerical
analysis. Their treatment of ODEs in particular bears little resemblance
to what is "state-of-the-art".

 Two reviews by numerical analysts are:
(1) Lawrence F. Shampine, "Review of 'Numerical Recipes, The Art of Scientific
    Computing'," The American Mathematical Monthly 94, 9 (Nov 87) 889-892.
(2) Richard J. Hanson "Cooking with 'Numerical Recipes' on a PC," SIAM (Society
    for Industrial and Applied Mathematics) News 28, 3 (May 90) 18.

Richard.
-- 
** R.W. Brankin -- Numerical Algorithms Group Ltd. -- nagrwb@vax.ox.ac.uk **
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