# An algebraic theory of order

Philippe Chartier; Ander Murua

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

- Volume: 43, Issue: 4, page 607-630
- ISSN: 0764-583X

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topChartier, Philippe, and Murua, Ander. "An algebraic theory of order." ESAIM: Mathematical Modelling and Numerical Analysis 43.4 (2009): 607-630. <http://eudml.org/doc/250616>.

@article{Chartier2009,

abstract = {
In this paper, we present an abstract framework which describes algebraically the derivation of order conditions independently of the nature of differential equations considered or the type of integrators used to solve them. Our structure includes a Hopf algebra of functions, whose properties are used to answer several questions of prime interest in numerical analysis. In particular, we show that, under some mild assumptions, there exist integrators of arbitrarily high orders for arbitrary (modified) vector fields.
},

author = {Chartier, Philippe, Murua, Ander},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Order conditions; Hopf algebra; group of abstract integration schemes; Lie algebra; composition.; order conditions; composition},

language = {eng},

month = {7},

number = {4},

pages = {607-630},

publisher = {EDP Sciences},

title = {An algebraic theory of order},

url = {http://eudml.org/doc/250616},

volume = {43},

year = {2009},

}

TY - JOUR

AU - Chartier, Philippe

AU - Murua, Ander

TI - An algebraic theory of order

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2009/7//

PB - EDP Sciences

VL - 43

IS - 4

SP - 607

EP - 630

AB -
In this paper, we present an abstract framework which describes algebraically the derivation of order conditions independently of the nature of differential equations considered or the type of integrators used to solve them. Our structure includes a Hopf algebra of functions, whose properties are used to answer several questions of prime interest in numerical analysis. In particular, we show that, under some mild assumptions, there exist integrators of arbitrarily high orders for arbitrary (modified) vector fields.

LA - eng

KW - Order conditions; Hopf algebra; group of abstract integration schemes; Lie algebra; composition.; order conditions; composition

UR - http://eudml.org/doc/250616

ER -

## References

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