NAG routine D02BAF uses runge-kutta-MERSON ??

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#1003

From: Fred Walsteijn
Date: Mon, 04 Jan 1993 14:13

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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).

Thanks for any clarifying remarks...
-----------------------------------------------------------------------------
Fred Walsteijn                                | Internet: walsteyn@fys.ruu.nl
Institute for Marine and Atmospheric Research | FAX:      31-30-543163
Utrecht University, The Netherlands           | Phone:    31-30-533169

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Path: arc1-ca.pugleaf.net!sparky!uunet!mcsun!sun4nl!ruuinf!ruunfs.fys.ruu.nl!walsteyn
From: walsteyn@fys.ruu.nl (Fred Walsteijn)
Subject: NAG routine D02BAF uses runge-kutta-MERSON ??
Message-ID: <1993Jan4.141352.5937@fys.ruu.nl>
Summary: is it the Merson routine mentioned in the textbooks ?
Keywords: Merson, nonlinear problems
Organization: Physics Department, University of Utrecht, The Netherlands
Date: Mon, 4 Jan 1993 14:13:52 GMT
Lines: 18