Geodesic
Solution for a classical problem in the calculus of variations via rationalized Haar functions
Kybernetika, Tome 37 (2001) no. 5, p. [575].

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A numerical technique for solving the classical brachistochrone problem in the calculus of variations is presented. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Application of this method results in the transformation of differential and integral expressions into some algebraic equations to which Newton-type methods can be applied. The method is general, and yields accurate results.
Classification : 49J15, 49K15, 49M30, 65K10, 70Q05
Keywords: variational problem; brachistochrone problem; nonlinear optimal control problem 
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     author = {Razzaghi, Mohsen and Ordokhani, Yadollah},
     title = {Solution for a classical problem in the calculus of variations via rationalized {Haar} functions},
     journal = {Kybernetika},
     pages = {[575]},
     publisher = {mathdoc},
     volume = {37},
     number = {5},
     year = {2001},
     mrnumber = {1877075},
     zbl = {1265.49023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2001__37_5_a3/}
}
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Razzaghi, Mohsen; Ordokhani, Yadollah. Solution for a classical problem in the calculus of variations via rationalized Haar functions. Kybernetika, Tome 37 (2001) no. 5, p. [575]. http://geodesic.mathdoc.fr/item/KYB_2001__37_5_a3/