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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}