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Solution of variational problems via hybrid of block-pulse and Lagrange interpolating

Solution of variational problems via hybrid of block-pulse and Lagrange interpolating

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  • Author(s): H.R. Marzban 1 ; H.R. Tabrizidooz 1 ; M. Razzaghi 2, 3
    • View affiliations
    • Affiliations: 1: Department of Mathematics, Isfahan University of Technology, Isfahan, Iran
      2: Department of Mathematics and Statistics, Mississippi State University, Mississippi State, USA
      3: Department of Applied Mathematics, Amirkabir University of Technology, Tehran, Iran
  • Source: Volume 3, Issue 10, October 2009, p. 1363 – 1369
    DOI:  10.1049/iet-cta.2008.0461 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

A direct method for solving variational problems using the hybrid of block-pulse functions and Lagrange interpolating polynomials is presented. The method is based upon hybrid functions approximations. The properties of hybrid functions, which consist of block-pulse functions and Lagrange interpolating polynomials, are presented. These properties are then utilised to reduce the variational problems to the solution of non-linear equations. Three examples are considered, in the first example the classical brachistochrone problem is studied and in the second and third examples, two non-linear problems are examined. The method is general, easy to implement and yields very accurate results.

Inspec keywords: nonlinear equations; polynomials; variational techniques; interpolation

Other keywords: Lagrange interpolating polynomial; block-pulse interpolation; block-pulse function; nonlinear problem; classical brachistochrone problem; variational problem; nonlinear equation; hybrid functions approximation

Subjects: Nonlinear and functional equations (numerical analysis); Interpolation and function approximation (numerical analysis); Interpolation and function approximation (numerical analysis); Nonlinear and functional equations (numerical analysis); Algebra, set theory, and graph theory; Numerical approximation and analysis

References

    1. 1)
      • A. Saadatmandi , M. Dehghan . The numerical solution of problems in calculus of variation using Chebyshev finite difference method. Phys. Lett. A , 4037 - 4040
    2. 2)
      • P. Dyer , S.R. McReynolds . (1970) The computation and theory of optimal control.
    3. 3)
      • J. Gregory , R.S. Wang . Discrete variable methods for the m-dependent variable nonlinear extremal problems in the calculus of variations. SIAM J. Numer. Anal. , 470 - 487
    4. 4)
      • C.F. Chen , C.H. Hsiao . A Walsh series direct method for solving variational problems. J. Franklin Inst. , 265 - 280
    5. 5)
      • R. Weinstock . (1952) Calculus of variations.
    6. 6)
      • A.V. Balakrishnan , L.W. Neustadt . (1964) Computing methods in optimization problems.
    7. 7)
      • R.Y. Chang , M.L. Wang . Shifted Legendre direct method for variational problems. J. Optim. Theory Appl. , 299 - 307
    8. 8)
      • C. Hwang , Y.P. Shih . Laguerre series direct method for variational problems. J. Optim. Theory Appl. , 143 - 149
    9. 9)
      • A.E. Bryson , Y.C. Ho . (1969) Applied optimal control.
    10. 10)
      • R. Bellman . (1957) Dynamic programming.
    11. 11)
      • J. Vlassenbroeck , R. Van Dooren . A new look at the brachistochrone problem. J. Appl. Math. Phys. (ZAMP) , 785 - 790
    12. 12)
      • F.R. Gantmacher . (1974) Theory of matrices.
    13. 13)
      • I.R. Horng , J.H. Chou . Shifted Chebyshev direct method for solving variational problems. Int. J. Syst. Sci. , 855 - 861
    14. 14)
      • M. Razzaghi , M. Razzaghi . Fourier series direct method for variational problems. Int. J. Control , 887 - 895
    15. 15)
      • P.J. Davis , P. Rabinowitz . (1975) Methods of Numerical Integration.
    16. 16)
      • D.S. Szarkowicz . Investigating the brachistochrone with a multistage Monte Carlo method. Int. J. Syst. Sci. , 233 - 243
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