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Title: Computing ODE symmetries as abnormal variational symmetries
Author: Gouveia, Paulo D.F.
Torres, Delfim F.M.
Keywords: Symmetries
Variational symmetries
Dynamic symmetries
Computer algebra systems
Optimal control
Issue Date: 2009
Publisher: Elsevier
Citation: Gouveia, Paulo D.F.; Torres, Delfim F.M. (2009) - Computing ODE symmetries as abnormal variational symmetries. Nonlinear Analysis: Theory, Methods & Applications. ISSN 0362-546X. 71:12, p. e138-e146
Abstract: 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 [P.D.F. Gouveia, D.F.M. Torres, Automatic computation of conservation laws in the calculus of variations and optimal control, Comput. Methods Appl. Math. 5 (4) (2005) 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 one 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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