This article is cited in 2 papers

Polynomial first-order differential equations over matrix skew series

V. P. Derevenskii

Chair of Higher Mathematics, Kazan State University of Architecture and Building, 1 Zelyonaya str., Kazan, 420043 Russia

Abstract: In this paper we establish that a solution to matrix ordinary first-order differential equations with polynomial right side can be reduced to integration of analogous scalar equations if its parameters are triangle. We give conditions upon elements of the sought-for matrix in the case when its parameters are given in the form of dual-diagonal matrices. We consider the Riccati equation over a set of square matrices of the third order. The results are expressed in terms of skew series introduced by the author earlier.

Keywords: matrix differential equations, decreasing of the order, skew series.

UDC: 517.9

Received: 23.02.2013

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:9, 1–12

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