Электронный каталог

Статья

Malykh, M.D.
Calculation of Modified Hamiltonian in Sage / M.D.Malykh, M.A.Konyaeva. – Text : electronic // Discrete and Continuous Models and Applied Computational Science. – 2026. – Vol. 34, No. 2. – P. 214-225. – URL: https://doi.org/10.22363/2658-4670-2026-34-2-214-225. – Bibliogr.: 23.

The algebraic properties of difference approximations of Hamiltonian systems are investigated. Sym-plectic schemes exactly preserve linear and quadratic integrals by virtue of Cooper’s theorem, but not the totalmechanical energy of nonlinear systems. However, it is known that instead of energy, symplectic differenceschemes preserve with a given order of approximation a quantity that goes over into the Hamiltonian as thetime step tends to zero. The paper presents an algorithm for calculating such a modified Hamiltonian and its im-plementation in the Sage computer algebra system for a given symplectic difference scheme, the required orderof energy conservation, and the Hamiltonian of the original mechanical system. The program successfully re-produces formulas previously derived manually, which confirms its consistency. Numerical experiments showthat solutions obtained using symplectic schemes closely coincide with the level lines of the modified Hamilton-ian, which emphasizes its role in preserving the qualitative behavior of the system during numerical integrationover large time intervals



Спец.(статьи,препринты) = С 17 и1 - Математическое моделирование
Спец.(статьи,препринты) = Ц 840 д - Аналитические вычисления на ЭВМ$
ОИЯИ = ОИЯИ (JINR)2026