Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Lie symmetries and differential Galois groups of linear equations

Author(s): W. R. Oudshoorn; M. van der Put.
Journal: Math. Comp. 71 (2002), 349-361.
MSC (2000): Primary 34A30, 34G34, 34Mxx, 65L99
Posted: October 4, 2001
MathSciNet review: 1863006
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Abstract | References | Similar articles | Additional information

Abstract: For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In connection with this a new algorithm for computing the Lie symmetries of a linear ordinary differential equation is presented.

References:

[K]: I. Kaplansky, An introduction to differential algebra, Second edition, Hermann, Paris, 1976. MR 57:297
[KM]: J. Krause and L. Michel, Équations différentielles linéaires d'ordre ayant une algèbre de Lie de symmétrie de dimension , C.R. Acad. Sci. Paris Sér. I Math. 307 (1988), 905-910. MR 89m:58183
[L1]: S. Lie, Vorlesungen über continuierliche Gruppen mit geometrischen und anderen Anwendungen, Bearbeitet und herausgegeben von Dr. G. Scheffers, Teubner, Leipzig, 1893.
[L2]: S. Lie, Klassifikation und Integration von gewöhnlicher Differentialgleichungen zwischen , die eine Gruppe von Transformationen gestetten I, Math. Ann. 22 (1888), 213-253.
[ML]: F.M. Mahomed and P.G.L. Leach, Symmetry Lie algebras of th order ordinary differential equations, J. Math. Anal. Appl. 151 (1990), 80-107.
[O1]: P.J. Olver, Applications of Lie groups to differential equations, Springer Verlag, New York, 1986. MR 88f:58161
[O2]: P.J. Olver, Equivalence, invariants and symmetry. Cambridge University Press, Cambridge, 1995. MR 96i:58005
[P]: M. van der Put, Galois theory of differential equations, algebraic groups and Lie algebras. Differential algebra and differential equations. J. Symbolic Comput. 28 (1999), 441-472. MR 2001b:12012
[St]: H. Stephani, Differential equations. Their solution using symmetries, Cambridge University Press, Cambridge, 1989. MR 91a:58001

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