Article: Backward error analysis and the substitution law for Lie group integrators
Author: Alexander Lundervold, Hans Z. Munthe-Kaas
Journal: Foundations of Computational Mathematics 2013 (2), 161-186.
Abstract: Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. 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 Lie--Butcher series. This paper presents the algebraic theory of backward error analysis for methods based on Lie--Butcher series.
Remarks in hindsight: None yet.
6 Jun 2011