🚀 go-pugleaf

In article <1993Jan4.141352.5937@fys.ruu.nl> walsteyn@fys.ruu.nl (Fred Walsteijn) writes:
>I have just read that the NAG routine D02BAF is based on
>a Runge-Kutta-Merson embedded formula.
>Is it the same formula as mentioned in the books of
>Lambert (1991) and Butcher (1987) ?
>
>If it is, does that mean that its error truncation estimate
>is ``easily defeated'' (cite, as I remember it from one of
>the abovementioned books) ?
>The reason is that the ``high order'' component has a high
>(fifth) order of accuracy only for linear problems.
>It cannot have fifth order of accuracy for all (e.g. nonlinear) problems
>as it has only five stages (Butcher, 1987).
>

I believe the formulas are the same, though it would be easy enough
to check the NAG documentation to find out.  Shampine showed that 
Merson's pair for general non-linear problems can be viewed as a (3,4) 
pair (i.e. embedded formulas of orders 3 and 4) with a certain "safety" 
factor multiplying the error estimate.  It has been used extensively for 
non-linear problems and generally performs well.  
-- 
Regards,
Mike Hosea (mhosea@seas.smu.edu)