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Author: search.filters.author.Meleshko, Sergey

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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.
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    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.
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    On first integrals of second-order ordinary differential equations
    (Springer, 2013-01-08) Meleshko, Sergey; Moyo, Sibusiso; Muriel, C.; Romero, J. L.; Guha, P.; Choudhury, A. G.
    Here we discuss first integrals of a particular representation associated with second-order ordinary differential equations. The linearization problem is a particular case of the equivalence problem together with a number of related problems such as defining a class of transformations, finding invariants of these transformations, obtaining the equivalence criteria, and constructing the transformation. The relationship between the integral form, the associated equations, equivalence transformations, and some examples are considered as part of the discussion illustrating some important aspects and properties.