Prof. Paulo Gouveia: New Applications
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en-us2022 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 17 Jan 2022 23:04:53 GMTMon, 17 Jan 2022 23:04:53 GMTNew applications published by Prof. Paulo Gouveiahttps://www.maplesoft.com/images/Application_center_hp.jpgProf. Paulo Gouveia: New Applications
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Computing ODE symmetries as abnormal variational symmetries
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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.<img src="https://www.maplesoft.com/view.aspx?si=6881/1.jpg" alt="Computing ODE symmetries as abnormal variational symmetries" style="max-width: 25%;" align="left"/>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.https://www.maplesoft.com/applications/view.aspx?SID=6881&ref=FeedTue, 11 Nov 2008 00:00:00 ZProf. Delfim TorresProf. Delfim TorresAutomatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control
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We present analytic computational tools that permit us to identify, in an automatic way, conservation laws in optimal control. The central result we use is the famous Noetherâ€™s theorem, a classical theory developed by Emmy Noether in 1918, in the context of the calculus of variations and mathematical physics, and which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in finding the symmetries and corresponding conservation laws in optimal control theory, thus making useful in practice the theoretical results recently obtained in the literature. A Maple implementation is provided and several illustrative examples given.<img src="https://www.maplesoft.com/view.aspx?si=4805/gouveia-torres-CLsOptCont_5.gif" alt="Automatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control" style="max-width: 25%;" align="left"/>We present analytic computational tools that permit us to identify, in an automatic way, conservation laws in optimal control. The central result we use is the famous Noetherâ€™s theorem, a classical theory developed by Emmy Noether in 1918, in the context of the calculus of variations and mathematical physics, and which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in finding the symmetries and corresponding conservation laws in optimal control theory, thus making useful in practice the theoretical results recently obtained in the literature. A Maple implementation is provided and several illustrative examples given.https://www.maplesoft.com/applications/view.aspx?SID=4805&ref=FeedWed, 26 Jul 2006 00:00:00 ZProf. Delfim TorresProf. Delfim Torres