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The aim is to extend the algebraic framework for deriving conserved quantities to arbitrary order ODE discretizations.

Conserved quantities of discretizations by polarization

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The aim is to extend the algebraic framework for deriving conserved quantities to arbitrary order ODE discretizations.
Introduced unconventional integrators based on polarization for higher order ODEs.
Extended previously proposed algebraic methods for deriving integrals of motion.
Explored discretizations of ODEs of all orders greater than or equal to 3.
New integrals of motion were identified for higher order ODEs (order ≥ 3).
Polarization discretization maintains conservation properties for Hamiltonian systems.
Invariant volume forms were established for first and second order Hamiltonian ODEs.

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This note reports new integral properties in discretizations of higher order ODEs, suggesting enhancements in integration methods.

Gießing et al. (2026) studied this question.

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