Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)3751810.22363/2658-4670-2023-31-4-387-398EATOFGArticlesСтатьиResearch ArticleOn a set of tests for numerical methods of integrating differential equations, based on the Calogero systemО наборе тестов для численных методов интегрирования дифференциальных уравнений, основанном на системе Калоджероhttps://orcid.org/0000-0001-6541-66036602318510P-8123-2016MalykhMikhail D.МалыхМ. Д.

Doctor of Physical and Mathematical Sciences, Assistant Professor

malykh_md@rudn.ruhttps://orcid.org/0009-0007-6504-8370ShiweiWangШивэйВан

Ph.D. student

1995wsw@gmail.comhttps://orcid.org/0000-0002-4105-2566YingYuИнЮй

Assistant Professor of Department of Mathematics and Applied Mathematics

45384377@qq.comRUDN UniversityРоссийский университет дружбы народовJoint Institute for Nuclear ResearchОбъединённый институт ядерных исследованийKaili UniversityУниверситет Кайли15122023314VOL 31, NO4 (2023)ТОМ 31, №4 (2023)38739819012024Copyright ©; 2023, Malykh M.D., Shiwei W., Ying Y.Copyright ©; 2023, Малых М.Д., Шивэй В., Ин Ю.2023Malykh M.D., Shiwei W., Ying Y.Малых М.Д., Шивэй В., Ин Ю.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/37518

Based on the completely integrable Calogero dynamical system, which describes the one-dimensional many-body problem, a tool for testing difference schemes has been developed and implemented in the original fdm package integrated into the Sage computer algebra system. This work shows how the developed tools can be used to examine the behavior of numerical solutions near the collision point and how to study the conservatism of the difference scheme. When detecting singularities using Alshina’s method, a difficulty was discovered associated with false order fluctuations. One of the main advantages of this set of tests is the purely algebraic nature of the solutions and integrals of motion.

На основе вполне интегрируемой динамической системы Калоджеро, описывающей одномерную задачу многих тел, разработан инструмент для тестирования разностных схем и реализован в оригинальном пакете fdm, интегрируемом в систему компьютерной алгебры Sage. Показано, как использовать разработанные инструменты для проверки поведения численных решений возле точек столкновения, а также для исследования консервативности разностных схем. При обнаружении особенностей по методу Альшиной обнаружена трудность, связанная с ложными колебаниями порядка. Одно из главных достоинств этого набора теста - чисто алгебраический характер решений и интегралов движения.

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