Gouveia, Paulo D.F.Torres, Delfim F.M.2010-01-272010-01-272009Gouveia, 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-e146http://hdl.handle.net/10198/1509We 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.engSymmetriesVariational symmetriesDynamic symmetriesODEsComputer algebra systemsOptimal controlAbnormalityjournal article