On a set of tests for numerical methods of integrating differential equations, based on the Calogero system

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Abstract

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.

About the authors

Mikhail D. Malykh

RUDN University; Joint Institute for Nuclear Research

Author for correspondence.
Email: malykh_md@rudn.ru
ORCID iD: 0000-0001-6541-6603
Scopus Author ID: 6602318510
ResearcherId: P-8123-2016

Doctor of Physical and Mathematical Sciences, Assistant Professor

6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation; 6 Joliot-Curie St., Dubna, 141980, Russian Federation

Wang Shiwei

RUDN University

Email: 1995wsw@gmail.com
ORCID iD: 0009-0007-6504-8370

Ph.D. student

6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation

Yu Ying

Kaili University

Email: 45384377@qq.com
ORCID iD: 0000-0002-4105-2566

Assistant Professor of Department of Mathematics and Applied Mathematics

3 Kaiyuan Rd., Kaili, 556011, People’s Republic of China

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