Geodesic
Integration of systems of ordinary differential equations with a small parameter which admit approximate Lie algebras
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 2, pp. 143-160

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The algorithm for the order reduction of ordinary differential equations (ODEs) by using the operator of invariant differentiation (OID) of admitted Lie algebra is modified for systems of ODEs with a small parameter that admit approximate Lie algebras of operators. Invariant representations of second-order ODEs and systems of two second-order ODEs are presented. The OID of approximate Lie algebra is introduced. It is shown that it is possible to construct a special type of OID, which is used for obtaining the first integral of the system considered. Examples of using the algorithm for cases of complete and incomplete inheritance of a Lie algebra are given.
Keywords: systems of odes with a small parameter, approximate Lie algebras, invariant representation, operator of invariant differentiation. 
A. A. Gainetdinova. Integration of systems of ordinary differential equations with a small parameter which admit approximate Lie algebras. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 2, pp. 143-160. http://geodesic.mathdoc.fr/item/VUU_2018_28_2_a1/
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