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Nonclassical pseudospectral method for the solution of brachistochrone problem

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  • Alipanah, A.
  • Razzaghi, M.
  • Dehghan, M.

Abstract

In this paper, nonclassical pseudospectral method is proposed for solving the classic brachistochrone problem. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Properties of nonclassical pseudospectral method are presented, these properties are then utilized to reduce the computation of brachistochrone problem to the solution of algebraic equations. Using this method, the solution to the brachistochrone problem is compared with those in the literature.

Suggested Citation

  • Alipanah, A. & Razzaghi, M. & Dehghan, M., 2007. "Nonclassical pseudospectral method for the solution of brachistochrone problem," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1622-1628.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:5:p:1622-1628
    DOI: 10.1016/j.chaos.2006.04.071
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    1. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
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