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 Mania 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.