
Journal of Lie Theory 31 (2021), No. 3, 625635 Copyright Heldermann Verlag 2021 On Computing Linearizing Coordinates from the Symmetry Algebra Sajid Ali Dept. of Mathematics and Statistics, College of Natural and Health Sciences, Zayed University, Dubai, UAE and: School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Islamabad, Pakistan sajid.ali@zu.ac.ae Hassan Azad Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan hassan.azad@sms.edu.pk Said Waqas Shah Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan waqas.shah@sms.edu.pk Fazal M. Mahomed DSINRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa and: School of Mathematics and Statistics, University of New South Wales, Sydney, Australia fazal.mahomed@wits.edu.za A characterization of the symmetry algebra of the Nthorder ordinary differential equations (ODEs) with maximal symmetry and all thirdorder linearizable ODEs is given. This is used to show that such an algebra g determines  up to a point transformation  only one linear equation whose symmetry algebra is g and an algorithmic procedure is given to find the linearizing coordinates. This procedure is applied to several examples from the literature. Keywords: Ordinary differential equations, linearization, vector fields, Lie algebras. MSC: 34A26, 37C10, 57R30. [ Fulltextpdf (133 KB)] for subscribers only. 