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Lie symmetries and differential Galois groups of linear equations

Authors: W. R. Oudshoorn and M. van der Put
Journal: Math. Comp. 71 (2002), 349-361
MSC (2000): Primary 34A30, 34G34, 34Mxx, 65L99
Published electronically: 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.

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Additional Information

W. R. Oudshoorn
Affiliation: Prinsengracht 275 Den Haag, The Netherlands

M. van der Put
Affiliation: Department of Mathematics, P.O. Box 800, 9700 AV, Groningen, The Netherlands

Received by editor(s): October 13, 1999
Received by editor(s) in revised form: January 24, 2000
Published electronically: October 4, 2001
Article copyright: © Copyright 2001 American Mathematical Society