Helmholtz's inverse problem of the discrete calculus of variations

Loïc Bourdin; Jacky Cresson

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arXiv · 1203.1209

Helmholtz's inverse problem of the discrete calculus of variations

Loïc Bourdin·Jacky Cresson

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Abstract

We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide the class of all possible Lagrangian formulations.

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Loïc Bourdin, Jacky Cresson. 2012-03-06. Helmholtz's inverse problem of the discrete calculus of variations. https://arxiv.org/abs/1203.1209

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