Algebraic structure of space and field.

Khukhunashvili, Z.V.; Khukhunashvili, Z.Z.

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Alternative analysis generated by a differential equation.

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Generalization of Okamoto's equation to arbitrary $2 \times 2$ Schlesinger system.

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An algebraic theory of order

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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...