Hartley Series Direct Method for Variational Problems

Document Type: Original Scientific Paper

Author

‎Department of Applied Mathematics, ‎Faculty of Mathematical Sciences, ‎University of Kashan, ‎Kashan‎, ‎I R Iran

Abstract

The computational method based on using the operational matrix of an
orthogonal function for solving variational problems is computer
oriented. In this approach, a truncated Hartley series together with
the operational matrix of integration and integration of the cross
product of two cas vectors are used for finding the solution of
variational problems. Two illustrative examples are included to
demonstrate the validity and applicability of the technique.

Keywords

Main Subjects


1. R. N. Bracewell, The Hartley Transform, Oxford University Press, New York,
1986.

2. C. Hwang, Y. P. Shih, Laguerre series direct method for variational problems,
J. Optim. Theory Appl. 39(1) (1983) 143–149.

3. H. R. Marzban, H. R. Tabrizidooz, M. Razzaghi, Solution of variational problems via hybrid of block-pulse and Lagrange interpolating, IET Control Theory Appl. 3(10) (2009) 1363–1369.

4. J. J. R. Melgoza, G. T. Heydt, A. Keyhani, B. L. Agrawal, D. Selin, Synchronous machine parameter estimation using the Hartley series, IEEE
Trans. Energy Conversion
16(1) (2001) 49–54.

5. K. J. Olejniczak, G. T. Heydt, Scanning the special section on the Hartley
transform,
Proc. IEEE 82(3) (1994) 372–380.

6. M. Razzaghi, Y. Ordokhani, An application of rationalized Haar functions for
variational problems,
Appl. Math. Comput. 122(3) (2001) 353–364.

7. M. Razzaghi, S. Yousefi, Legendre wavelets direct method for variational problems, Math. Comput. Simulation 53(3) (2000) 185–192.

8. A. Saadatmandi, T. Abdolahi-Niasar, An analytic study on the EulerLagrange equation arising in calculus of variations, Comput. Methods Differ.
Equ.
2(3) (2014) 140–152.

9. A. Saadatmandi, M. Dehghan, The numerical solution of problems in calculus
of variation using Chebyshev finite difference method,
Phys. Lett. A 372(22)
(2008) 4037–4040.

10. A. Saadatmandi, M. Razzaghi, M. Dehghan, Hartley series approximations
for the parabolic equations,
Int. J. Comput. Math. 82(9) (2005) 1149–1156.

11. R. S. Schechter, The Variational Method in Engineering, Mc Graw-Hill,
NewYork, 1967.

12. M. Tatari, M. Dehghan, Solution of problems in calculus of variations via He’s
variational iteration method,
Phys. Lett. A 362(5–6) (2007) 401–406.