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.
@article{VUU_2018_28_2_a1,
author = {A. A. Gainetdinova},
title = {Integration of systems of ordinary differential equations with a small parameter which admit approximate {Lie} algebras},
journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
pages = {143--160},
publisher = {mathdoc},
volume = {28},
number = {2},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VUU_2018_28_2_a1/}
}
TY - JOUR AU - A. A. Gainetdinova TI - Integration of systems of ordinary differential equations with a small parameter which admit approximate Lie algebras JO - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki PY - 2018 SP - 143 EP - 160 VL - 28 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VUU_2018_28_2_a1/ LA - ru ID - VUU_2018_28_2_a1 ER -
%0 Journal Article %A A. A. Gainetdinova %T Integration of systems of ordinary differential equations with a small parameter which admit approximate Lie algebras %J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki %D 2018 %P 143-160 %V 28 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/VUU_2018_28_2_a1/ %G ru %F VUU_2018_28_2_a1
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/