Complete group classification of systems of two linear second-order ordinary differential equations : the algebraic approach
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We give a complete group classiﬁcation of the general case of linear systems of two second-order ordinary differential equations. The algebraic approach is used to solve the group classiﬁcation problem for this class of equations. This completes the results in the literature on the group classiﬁcation of two linear second-order ordinary differential equations including recent results which give a complete group classiﬁcation treatment of such systems. We show that using the algebraic approach leads to the study of a variety of cases in addition to those already obtained in the literature. We illustrate that this approach can be used as a useful tool in the group classiﬁcation of this class of equations. A discussion of the subsequent cases and results is given. Copyright © 2014 John Wiley & Sons, Ltd.
Mkhize, T.G.; Moyo, S. and Meleshko, S. V. 2013. Complete group classification of systems of two linear second-order ordinary differential equations: the algebraic approach. Mathematical Methods in the Applied Sciences. DOI: 10.1002/mma.3193