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This paper deals with the convergence and dynamics of Chebyshev's method for simple and multiple zeros of analytic functions. We establish a local convergence theorem that provides error estimates and exact domains of initial approximations to guarantee the Q-cubic convergence of the method right from the first iteration. Applications to some real-world problems as well as theoretical and numerical comparison with the famous Halley's method are also provided. [ABSTRACT FROM AUTHOR]

In this paper, we unify the study of the geodesics in the Bondi- Gold-Hoyle universe model. Thus, we obtain analytical solutions of the geodesic equations which describe the motion of space-like, time-like and light-like particles in the considered model. In the case of light-like geodesics, we get the solutions obtained by Marcheva & Ivanov, 2017. [ABSTRACT FROM AUTHOR]

A general optimal iterative method, for approximating the solution of nonlinear equations, of (n + 1) steps with 2 n + 1 order of convergence is presented. Cases n = 0 and n = 1 correspond to Newton's and Ostrowski's schemes, respectively. The basins of attraction of the proposed schemes on different test functions are analyzed and compared with the corresponding to other known methods. The dynamical planes showing the different symmetries of the basins of attraction of new and known methods are presented. The performance of different methods on some test functions is shown. [ABSTRACT FROM AUTHOR]