Publicação
Computing ODE symmetries as abnormal variational symmetries
| Resumo: | 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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| Autores principais: | Gouveia, Paulo D.F. |
| Outros Autores: | Torres, Delfim F.M. |
| Assunto: | Symmetries Variational symmetries Dynamic symmetries ODEs Computer algebra systems Optimal control Abnormality |
| Ano: | 2008 |
| País: | Portugal |
| Tipo de documento: | working paper |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Politécnica de Bragança |
| Idioma: | inglês |
| Origem: | Biblioteca Digital da UPB |
| Resumo: | 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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