Computing ODE Symmetries as Abnormal Variational Symmetries

Details Computing ODE Symmetries as Abnormal Variational Symmetries Computing ODE Symmetries as Abnormal Variational Symmetries

2008-04-06

arxiv.org/abs/0804.0925v1

Nonlinear Anal. 71 (2009), no. 12, e138--e146

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1016/j.na.2008.10.009

We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [Comput. Methods Appl. Math. 5 (2005), no. 4, pp. 387-409], and is based on the resolution of a first order linear PDE that arises as a necessary and sufficient condition of invariance for abnormal optimal control problems. A computer algebra procedure is developed, which permits to obtain ODE symmetries by the proposed method. Examples are given, and results compared with those obtained by previous available methods.

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