The BCH-Formula and Order Conditions for Splitting Methods
Winfried Auzinger, Wolfgang Herfort, Othmar Koch, Mechthild Thalhammer
TL;DR
This paper derives order conditions for splitting schemes using the BCH-formula and non-commutative power series, providing a unified approach to analyze the accuracy of splitting methods.
Contribution
It introduces a novel application of the BCH-formula and Lyndon-Shirshov words to establish order conditions for splitting methods.
Findings
Order conditions are derived using the BCH-formula.
Equivalent conditions are obtained via Lyndon-Shirshov words.
The approach unifies different techniques for analyzing splitting schemes.
Abstract
As an application of the BCH-formula, order conditions for splitting schemes are derived. The same conditions can be obtained by using non-commutative power series techniques and inspecting the coefficients of Lyndon-Shirshov words.
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Taxonomy
TopicsMathematical functions and polynomials · Numerical methods for differential equations · Polynomial and algebraic computation