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# An Alternative Algorithm for the Symmetry Classification of Ordinary Differential Equations

Yi Tian1,2,*, Jing Pang3,4

1 College of Data Science and Application, Inner Mongolia University of Technology, Hohhot, 010080, China
2 Inner Mongolia Autonomous Region Engineering and Technology Research Center of Big Data Based Software Service, Hohhot, 010080, China
3 College of Science, Inner Mongolia University of Technology, Hohhot, 010051, China
4 Inner Mongolia Key Laboratory of Statistical Analysis Theory for Life Data and Neural Network Modeling, Inner Mongolia University of Technology, Hohhot, 010051, China

* Corresponding Author: Yi Tian. Email:

(This article belongs to this Special Issue: Analytical Methods for Nonlinear Vibration & Active Control in Nano/Micro Devices and Systems)

Sound & Vibration 2022, 56(1), 65-76. https://doi.org/10.32604/sv.2022.014547

## Abstract

This is the first paper on symmetry classification for ordinary differential equations (ODEs) based on Wu’s method. We carry out symmetry classification of two ODEs, named the generalizations of the Kummer-Schwarz equations which involving arbitrary function. First, Lie algorithm is used to give the determining equations of symmetry for the given equations, which involving arbitrary functions. Next, differential form Wu’s method is used to decompose determining equations into a union of a series of zero sets of differential characteristic sets, which are easy to be solved relatively. Each branch of the decomposition yields a class of symmetries and associated parameters. The algorithm makes the classification become direct and systematic. Yuri Dimitrov Bozhkov, and Pammela Ramos da Conceição have used the Lie algorithm to give the symmetry classifications of the equations talked in this paper in 2020. From this paper, we can find that the differential form Wu’s method for symmetry classification of ODEs with arbitrary function (parameter) is effective, and is an alternative method.

## Cite This Article

Tian, Y., Pang, J. (2022). An Alternative Algorithm for the Symmetry Classification of Ordinary Differential Equations. Sound & Vibration, 56(1), 65–76.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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