NDLI: Stage Value Predictors and Efficient Newton Iterations in Implicit Runge--Kutta Methods

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Sderlind, Gustaf Olsson, Hans
Copyright Year	1998
Abstract	The prediction of stage values in implicit Runge--Kutta methods is important both for overall efficiency as well as for the design of suitable control strategies for the method. The purpose of this paper is to construct good stage value predictors for implicit methods and to verify their behavior in practical computations. We show that for stiffly accurate methods of low stage order it is necessary to use several predictors. In other words, a continuous extension for the method will not yield the best results. We also investigate how to gain additional efficiency in the Newton iterations used to correct the prediction error. This leads to new control strategies with respect to refactorization of Jacobians that seek to globally minimize total work per unit time of integration.
Starting Page	185
Ending Page	202
Page Count	18
File Format	PDF
ISSN	10648275
DOI	10.1137/S1064827596306963
e-ISSN	10957197
Issue Number	1
Volume Number	20
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	predictors convergence Newton iteration implicit Runge--Kutta Initial value problems control strategies
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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