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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Applied Numerical Ma...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Applied Numerical Mathematics
Article . 2005 . Peer-reviewed
License: Elsevier TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 2005
Data sources: zbMATH Open
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Nordsieck representation of two-step Runge–Kutta methods for ordinary differential equations

Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations
Authors: Bartoszewski, Z.; Jackiewicz, Z.;

Nordsieck representation of two-step Runge–Kutta methods for ordinary differential equations

Abstract

Two-step Runge-Kutta methods are a generalization of classical one-step methods, where each integration step reuses quantities computed in the previous step. Although they can attain higher accuracy for a given number of function evaluations than for standard Runge-Kutta methods, they are less convenient to implement with variable stepsize. The authors propose to overcome this disadvantage by representing data passed from step to step in Nordsieck representation, that is using scaled derivatives up to the order of the method. This has additional advantages in that new reliable error estimators become available. The estimator is seen to be very accurate on numerical tests and the implementation overall, at least for low order methods in the new family, is seen to be competitive.

Related Organizations
Keywords

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, numerical examples, Nordsieck representation, error estimation, two-step Runge-Kutta methods, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, Error bounds for numerical methods for ordinary differential equations

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
19
Average
Top 10%
Top 10%
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