Article
Ufa Mathematical Journal
Volume 9, Number 4, pp. 12-21
Invariant differentiation operator and its application for integrating systems of ordinary differential equations
Gainetdinova A.A., Gazizov R.K.
DOI:10.13108/2017-9-4-12
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We introduce an algorithm for integrating $n$-th-order systems of ordinary differential equations admitting $n$-dimensional Lie algebras of operators. The algorithm is based on invariant representation of considered system by the invariants of admitting Lie algebra and the application of the operator of invariant differentiation of special type. We proved the existence of the operator of invariant differentiation of suggested type and gave the algorithm for its construction. The suggested algorithm is compared with the known methods of integrating the first and second-order equations. Also we illustrated the application of the algorithm to the integrating systems of ordinary differential equations by the example of a systems of two second-order equations.