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Complete group classification of systems of two linear second‐order ordinary differential equations: the algebraic approach
Author(s) -
Mkhize T. G.,
Moyo S.,
Meleshko S. V.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3193
Subject(s) - mathematics , differential algebraic equation , ordinary differential equation , group (periodic table) , differential algebraic geometry , class (philosophy) , variety (cybernetics) , differential equation , algebraic number , algebraic equation , linear differential equation , order (exchange) , algebra over a field , pure mathematics , mathematical analysis , nonlinear system , computer science , statistics , artificial intelligence , chemistry , physics , organic chemistry , finance , quantum mechanics , economics
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.