FUW TRENDS IN SCIENCE & TECHNOLOGY JOURNAL
(A Peer Review Journal)
e–ISSN: 2408–5162; p–ISSN: 2048–5170
keywords: Cost functional, nodal points, optimal control, optimal state, wave equation
The fourier solution proposed by Duchateau and Zachmann for deriving the general equations for states and controls was applied to the problems of one dimensional quadratic functionalMin ∫ [z,u] =Min 01 01 dxdt and the finite element technique used on the resulting system to obtain the states, controls and the cost functional at different levels of discretization up to ten nodal points. The numerical solutions depict increase in the cost functional as the space dimension increases while as the number of elements increase, the controls get smaller among other things.
Bawa M 2013. Implementation of the finite element technique to the optimal control of one dimensional energized wave equation. Int. Org. Scientific Res. (IOSR) J. Mathematics, 5(6): 31-38. Binder L 1911. Uber Aussere Wurmleitung und Erwrumung Elektrisc her Maschinen, Dissertation, Technische Hoschudle. W. Knapp Verlag, Halle, Munchen, Germany. Duchateau P & Zachmann DW 1986. Partial Differential Equations, 2nded. McGraw Hill, New York, NY, USA. Pain HJ 1976.The physics of vibrations and waves, 2nd edition, John Wiley and Sons. Raisinghania MD 2010. Advanced Differential Equations. Chand and Company Ltd, New Delhi. Rao SS 1989. The Finite Element Method in Engineering. Pergamon Press. Reju SA 1995. Computational Optimization in Mathematical Physics; Ph.D. Thesis, Univ. of Ilorin, Ilorin, Nigeria. Schmidt EA 1924. Fuppl.Festschrift. Springer Verlag, Berlin, Germany. Singh MA & Titli AJ 1978. System Decomposition, Optimization & Control. Pergamon, Toulouse, France.
