A numerical solution of the nonlinear controlled Duffing oscillator by radial basis functions
作者： J.A. Rad , S. Kazem , K. Parand
DOI: 10.1016/J.CAMWA.2012.03.104
关键词:
摘要: In this research, a new numerical method is applied to investigate the nonlinear controlled Duffing oscillator. This based on radial basis functions (RBFs) approximate solution of optimal control problem by using collocation method. We apply Legendre-Gauss-Lobatto points for RBFs center nodes in order use integration more easily; then Lagrange multipliers used obtain optimum problems. For purpose different applications are used. The differential and integral expressions which arise dynamic systems, performance index boundary conditions converted into some algebraic equations can be solved unknown coefficients. Illustrative examples included demonstrate validity applicability technique.
core.ac.uk
elsevier.com
acm.org 
sci-hub.se 参考文章(63)
Shmuel Rippa, An algorithm for selecting a good value for the parameter c in radial basis function interpolation Advances in Computational Mathematics. ,vol. 11, pp. 193- 210 ,(1999) , 10.1023/A:1018975909870
Gamal N. Elnagar, Mohammad A. Kazemi, Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems Computational Optimization and Applications. ,vol. 11, pp. 195- 217 ,(1998) , 10.1023/A:1018694111831
Holger Wendland, Scattered Data Approximation ,(2004)
Martin D. Buhmann, Radial Basis Functions: Theory and Implementations ,(2003)
K. Parand, S. Abbasbandy, S. Kazem, A.R. Rezaei, Comparison between two common collocation approaches based on radial basis functions for the case of heat transfer equations arising in porous medium Communications in Nonlinear Science and Numerical Simulation. ,vol. 16, pp. 1396- 1407 ,(2011) , 10.1016/J.CNSNS.2010.07.011
Mohsen Razzaghi, Hamid-Reza Marzban, Optimal control of singular systems via piecewise linear polynomial functions Mathematical Methods in The Applied Sciences. ,vol. 25, pp. 399- 408 ,(2002) , 10.1002/MMA.297
H.R Marzban, M Razzaghi, Numerical solution of the controlled Duffing oscillator by hybrid functions Applied Mathematics and Computation. ,vol. 140, pp. 179- 190 ,(2003) , 10.1016/S0096-3003(02)00112-1
Maithili Sharan, E.J. Kansa, Suman Gupta, Application of the multiquadric method for numerical solution of elliptic partial differential equations Applied Mathematics and Computation. ,vol. 84, pp. 275- 302 ,(1997) , 10.1016/S0096-3003(96)00109-9
K. Parand, S. Abbasbandy, S. Kazem, J.A. Rad, A novel application of radial basis functions for solving a model of first-order integro-ordinary differential equation Communications in Nonlinear Science and Numerical Simulation. ,vol. 16, pp. 4250- 4258 ,(2011) , 10.1016/J.CNSNS.2011.02.020
Mohsen Razzaghi, Gamal Elnagar, Numerical solution of the controlled Duffing oscillator by the pseudospectral method Journal of Computational and Applied Mathematics. ,vol. 56, pp. 253- 261 ,(1994) , 10.1016/0377-0427(94)90081-7