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On group classification of normal systems of linear second-order ordinary differential equations
(Elsevier, 2015-05) Moyo, Sibusiso; Meleshko, Sergey; Oguis, Giovanna Fae Ruiz
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results and subsequent theorem arising from this particular study are discussed here. This paper considers the study of irreducible systems of second-order ordinary differential equations.
On the group classiﬁcation of systems of two linear second-order ordinary differential equations with constant coeﬃcients
(Elsevier, 2014) Meleshko, Sergey; Moyo, Sibusiso; Oguis, Giovanna Fae Ruiz
The completeness of the group classiﬁcation of systems of two linear second-order ordinary differential equations with constant coeﬃcients is delineated in the paper. The new cases extend what has been done in the literature. These cases correspond to the type of equations where the commutative property of the coeﬃcient matrices with respect to the dependent variables and the ﬁrst-order derivatives in the considered system does not hold. A discussion of the results as well as a note on the extension to linear systems of second-order ordinary differential equations with more than two equations are given.