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Article #1021Re: NAG routine D02BAF uses runge-kutta-MERSON ??
From: Mike Hosea
Date: Tue, 05 Jan 1993 17:31
Date: Tue, 05 Jan 1993 17:31
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In article <1ia4m9INN2h2@rave.larc.nasa.gov> makarand@gazelle.larc.nasa.gov (Makarand A. Kulkarni) writes: >Most error estimates for integrators are based on what is called >the "linear test equation". It is extremely difficult if not >impossible to obtain local truncation error estimates for >nonlinear problems. Normally error estimates for nonlinear >problems are obtained by linearizing the equation(s). If I understand you correctly, this isn't true. Error estimators for integrators are usually based on subtracting a higher order result from a lower order result to get an asymptotically correct estimate of the error in the lower order result. The technique is valid for linear and nonlinear problems. You must be thinking about linear vs. general (nonlinear) stability analysis, since the "linear test equation" is used in that context, and general (nonlinear) stability analysis is a lot harder than the linear stability analysis. -- Regards, Mike Hosea (mhosea@seas.smu.edu)
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Newsgroups: sci.math.num-analysis Path: arc1-ca.pugleaf.net!sparky!uunet!seas.smu.edu!mhosea From: mhosea@seas.smu.edu (Mike Hosea) Subject: Re: NAG routine D02BAF uses runge-kutta-MERSON ?? Message-ID: <1993Jan5.173151.21651@seas.smu.edu> Keywords: Merson, nonlinear problems Sender: mhosea@seas.smu.edu Nntp-Posting-Host: express.seas.smu.edu Organization: SMU - School of Engineering & Applied Science - Dallas References: <1993Jan4.141352.5937@fys.ruu.nl> <1ia4m9INN2h2@rave.larc.nasa.gov> Date: Tue, 5 Jan 1993 17:31:51 GMT Lines: 21