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Home » Issues » Archive of Issues » 2018 - 2 issue » pp. 143-160

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Russia Ufa
Year
2018
Volume
28
Issue
2
Pages
143-160
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Section Mathematics
Title Integration of systems of ordinary differential equations with a small parameter which admit approximate Lie algebras
Author(-s) Gainetdinova A.A.a
Affiliations Ufa State Aviation Technical Universitya
Abstract 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
UDC 517.925
MSC 34A25, 22E05
DOI 10.20537/vm180202
Received 14 April 2018
Language Russian
Citation Gainetdinova A.A. Integration of systems of ordinary differential equations with a small parameter which admit approximate Lie algebras, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 2, pp. 143-160.
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