ISJ Theoretical & Applied Science 05(145) 2025

Philadelphia, USA

Krakhmaleva, Yu.R., Mukhambetzhanov, S.T., & Tursynova, T.

Finding a solution to the Lyapunov system using small parameter methods in Maple.

Full Article: PDF

Scientific Object Identifier: http://s-o-i.org/1.1/TAS-05-145-41

DOI: https://dx.doi.org/10.15863/TAS.2025.05.145.41

Language: Russian

Citation: Krakhmaleva, Yu.R., Mukhambetzhanov, S.T., & Tursynova, T. (2025). Finding a solution to the Lyapunov system using small parameter methods in Maple. ISJ Theoretical & Applied Science, 05 (145), 345-354. Soi: https://s-o-i.org/1.1/TAS-05-145-41 Doi: https://dx.doi.org/10.15863/TAS.2025.05.145.41

Pages: 345-354

Published: 30.05.2025

Abstract: The small parameter method has its own peculiarities in solving various problems. There are differences in the methods of constructing solutions for autonomous and non-autonomous systems, in the non-resonant case and near resonance, for quasi-linear systems and systems close to arbitrary nonlinear ones. In connection with the development of computer algebra, it is important to implement the small parameter method in the study of the motion of mechanical systems in modern mathematical packages, the dynamic development of which is currently being carried out successfully. The article describes a technique for finding solutions to the Duffing equation using the Poincare method and the Lyapunov method in the Maple environment.

Key words: Duffing equation, Poincare method, small parameter, Lyapunov method, Maple system.