NDLI: Backward Error Analysis and the Substitution Law for Lie Group Integrators

Content Provider	Springer Nature Link
Author	Lundervold, Alexander Munthe Kaas, Hans
Copyright Year	2012
Abstract	Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees, and can be used to represent a large class of numerical methods. The theory of backward error analysis for differential equations has a particularly nice description when applied to methods represented by Butcher series. For the study of differential equations evolving on more general manifolds, a generalization of Butcher series has been introduced, called the Lie–Butcher series. This paper presents the theory of backward error analysis for methods based on Lie–Butcher series.
Ending Page	186
Page Count	26
Starting Page	161
File Format	PDF
ISSN	16153375
e-ISSN	16153383
Journal	Foundations of Computational Mathematics
Issue Number	2
Volume Number	13
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-07-10
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Butcher series Lie group integrators Economics general Multistep, Runge-Kutta and extrapolation methods Backward error analysis Linear and Multilinear Algebras, Matrix Theory Substitution law Lie–Butcher series Rooted trees Numerical Analysis Computer Science Initial value problems Vector fields, flows, ordinary differential equations Applications of Mathematics Math Applications in Computer Science Hopf algebras
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Theory and Mathematics Computational Mathematics

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