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An Alternative Method for a Classical Problem in the Calculus of Variations
Author(s) -
Elnagar Gamal,
Razzaghi Mohsen
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19960910)19:13<1091::aid-mma813>3.0.co;2-a
Subject(s) - mathematics , chebyshev nodes , optimal control , interpolation (computer graphics) , transformation (genetics) , algebraic equation , polynomial , calculus (dental) , mathematical optimization , nonlinear system , mathematical analysis , computer science , animation , medicine , biochemistry , chemistry , physics , computer graphics (images) , dentistry , quantum mechanics , gene
A numerical technique for determining the solution of the brachistochrone problem is presented. The brachistochrone problem is first formulated as a non‐linear optimal control problem. Using Chebyshev nodes, we construct the M th degree polynomial interpolation to approximate the state and the control variables. Application of this method results in the transformation of differential and integral expressions into some non‐linear algebraic equations to which Newton‐type methods can be applied. Simulation studies demonstrate computational advantages relative to existing methods in the literature.