Электронный каталог

Статья

Lapshenkova, L.O.
On the Algebraic Properties of Difference Approximationsof Hamiltonian Systems / L.O.Lapshenkova, M.D.Malykh, E.N.Matyukhina. – Text : electronic // Discrete and Continuous Models and Applied Computational Science. – 2025. – Vol. 33, No. 3. – P. 260-271. – URL: https://doi.org/10.22363/2658-4670-2025-33-3-260-271. – Bibliogr.: 26.

In this paper, we examine difference approximations for dynamic systems characterized by polynomialHamiltonians, specifically focusing on cases where these approximations establish birational correspondencesbetween the initial and final states of the system. Difference approximations are commonly used numericalmethods for simulating the evolution of complex systems, and when applied to Hamiltonian dynamics, theypresent unique algebraic properties due to the polynomial structure of the Hamiltonian. Our approach involvesanalyzing the conditions under which these approximations preserve key features of the Hamiltonian system,such as energy conservation and phase-space volume preservation. By investigating the algebraic structureof the birational mappings induced by these approximations, we aim to provide insights into the stabilityand accuracy of numerical simulations in identifying the true behavior of Hamiltonian systems. The resultsoffer a framework for designing efficient and accurate numerical schemes that retain essential properties ofpolynomial Hamiltonian systems over time



Спец.(статьи,препринты) = С 17 в - Аппроксимационные методы. Эмпирические формулы
ОИЯИ = ОИЯИ (JINR)2025