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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2009

An algebraic theory of order

Philippe Chartier
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Ander Murua
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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.
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Dates and versions

hal-00777190 , version 1 (17-01-2013)

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Philippe Chartier, Ander Murua. An algebraic theory of order. ESAIM: Mathematical Modelling and Numerical Analysis, 2009, 43 (4), pp.607-630. ⟨10.1051/m2an/2009029⟩. ⟨hal-00777190⟩
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