The cohesiveness of G-symplectic methods
type: Item
instance of: scholarly article
title: The cohesiveness of G-symplectic methods
zbMATH Open document ID: 1330.65192
published in: Numerical Algorithms
publication date: 2015-11-17T00:00:00Z
review text: The author shortly reviews the G-symplectic methods, previously introduced by himself, provides an example of such method, the so-called 4123A method and illustrates the deleterious effect of parasitism. Then he is concerned with the G-symplectic methods with zero parasitic growth and introduces the concept of cohesiveness. This concept has been revealed in order ``to describe the holding together of the multiple values generated as output from one step''. For a G-symplectic method in partitioned diagonal form, the main result shows the slow growth of the deviation from cohesiveness. Eventually, it is numerically confirmed for the above mentioned method.
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 6510063
zbMATH Keywords: system of ODE
zbMATH Keywords: Cauchy problem
zbMATH Keywords: invariance
zbMATH Keywords: symplectic method
zbMATH Keywords: G-symplectic method
zbMATH Keywords: parasitic growth
zbMATH Keywords: one step method
zbMATH Keywords: internal starting
zbMATH Keywords: cohesiveness
zbMATH Keywords: Hénon-Heiles problem
author: J. C. Butcher
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
full work available at URL: s11075-015-9964-y
OpenAlex ID: W2094674053
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DOI: 10.1007/S11075-015-9964-Y
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description: scientific article; zbMATH DE number 6510063