Computing ODE symmetries as abnormal variational symmetries

• Author(s): Gouveia, Paulo D.F. ; Torres, Delfim F.M.
• Date: 2009
• Persistent ID: http://hdl.handle.net/10198/1509
• Origin: Biblioteca Digital do IPB
• Subject(s): Symmetries; Variational symmetries; Dynamic symmetries; ODEs; Computer algebra systems; Optimal control; Abnormality
• Document Type: Article
• Language: English

Description

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.