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Symmetry group classification of ordinary differential equations: Survey of some results
Author(s) -
Mahomed F. M.
Publication year - 2007
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.934
Subject(s) - mathematics , ordinary differential equation , group (periodic table) , symmetry (geometry) , separable partial differential equation , scalar (mathematics) , symmetry group , mathematical analysis , differential equation , order (exchange) , examples of differential equations , mathematical physics , pure mathematics , differential algebraic equation , geometry , physics , finance , quantum mechanics , economics
After the initial seminal works of Sophus Lie on ordinary differential equations, several important results on point symmetry group analysis of ordinary differential equations have been obtained. In this review, we present the salient features of point symmetry group classification of scalar ordinary differential equations: linear n th‐order, second‐order equations as well as related results. The main focus here is the contributions of Peter Leach, in this area, in whose honour this paper is written on the occasion of his 65th birthday celebrations. Copyright © 2007 John Wiley & Sons, Ltd.