Geodesic
Integration of systems of two second-order ordinary differential equations with a small parameter that admit four essential operators
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 604-614

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We discuss an algorithm for integrating systems of two second-order ordinary differential equations (ODE) with a small parameter that admit approximate Lie algebras with four essential generators. The algorithm is a modification of the method of consecutive order reduction and is based on using operators of invariant differentiation. A special attention is given to the peculiarities of its application in dependence of the structural properties of Lie algebras of approximate symmetries.
Keywords: system of two second-order ordinary differential equations with a small parameter, approximate Lie algebra of generators, operator of invariant differentiation, invariant representation, differential invariant, integration of equations. 
@article{SEMR_2020_17_a90,
     author = {A. A. Gainetdinova and R. K. Gazizov},
     title = {Integration of systems of two second-order ordinary differential equations with a small parameter that admit four essential operators},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {604--614},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a90/}
}
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A. A. Gainetdinova; R. K. Gazizov. Integration of systems of two second-order ordinary differential equations with a small parameter that admit four essential operators. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 604-614. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a90/