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A Discrete Algorithm to the Calculus of Variations

Celia T. L. M. Pereira, Pedro A. F. Cruz, Delfim F. M. Torres


A numerical study of an algorithm proposed by Gusein Guseinov, which determines approximations to the optimal solution of problems of calculus of variations using two discretizations and correspondent Euler-Lagrange equations, is investigated. The results we obtain to discretizations of the brachistochrone problem and Maniµa example with Lavrentiev's phenomenon are compared with the solutions found by other methods and solvers. We conclude that Guseinov's method presents better solutions in most of the cases studied.


calculus of variations, Euler-Lagrange equations, discretization, solvers, brachistochrone problem, Lavrentiev phenomenon, Mania example.

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