Numerical solution of the controlled Duffing oscillator by hybrid functions

Applied Mathematics and Computation

Volumn 140, Issue 2-3, 2003, Pages 179-190

  Marzban, H R ^a,c   Razzaghi, M ^a,b  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

^b MISSISSIPPI STATE UNIVERSITY   (United States)

^c ISFAHAN UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Duffing; Hybrid; Numerical; Oscillator

Indexed keywords

APPROXIMATION THEORY; MATRIX ALGEBRA; NONLINEAR SYSTEMS; POLYNOMIALS;

DUFFING OSCILLATORS;

OSCILLATORS (MECHANICAL);

EID: 0037431585     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00112-1     Document Type: Article

References (11)

1. Gille J.C., Decaulne P., Pelegrain M. Systems Asservis Non Lineaires. 1975;Bordas, Paris.
2. Nayfeh A.H., Mook D.T. Nonlinear Oscillations. 1979;Wiley, New York.
3. Vlassenbroeck J., Van Dooren R. Chebyshev Series Solution of the Controlled Duffing Oscillator. J. Comput. Phys. 47:1982;321-329.
4. Chen C.F., Hsiao C.H. Walsh series analysis in optimal control. Int. J. Contr. 21:1975;881-897.
5. Hsu N.S., Chang B. Analysis and optimal control of time-varying linear systems via block-pulse functions. Int. J. Contr. 33:1989;1107-1122.
6. Hwang C., Shih Y.P. Laguerre series direct method for variational problems. J. Optim. Theory Appl. 39:1983;143-149.
7. Chang R.Y., Wang M.L. Shifted Legendre series direct method for variational problems. J. Optim. Theory Appl. 39:1983;299-307.
8. Horng I.R., Chou J.H. Shifted Chebyshev series direct method for solving variational problems. Int. J. Sys. Sci. 16:1985;855-861.
9. Razzaghi M., Razzaghi M. Fourier series direct method for variational problems. Int. J. Contr. 48:1988;887-895.
10. Pontryagin L.S., Boltyanskii V., Gamkrelidze R., Mischenko E. The Mathematical Theory of Optimal Processes. 1962;Interscience, New York.
11. Razzaghi M., Marzban H.R. A hybrid analysis direct method in the calculus of variations. Int. J. Comput. Math. 75:2000;259-269.