Volume 9 Issue 1 - September 2017

  • 1. A six-order method based on heronian mean for solving non-linear equations

    Authors : Manoj Kumar Singh, Arvind K. Singh

    Pages : 158-165

    DOI : http://dx.doi.org/10.21172/1.91.24

    Keywords : Newton's method, Iteration function, Order of convergence, Function evaluations, Efficiency index

    Abstract :

    A new variant of Newton's method based on heronian mean has been developed and its convergence has been discussed. The method generates a sequence converging to the root with a suitable choice of initial approximation x_0. The convergence analysis shows that the proposed method has sixth order of convergence. In terms of computational cost, it requires evaluations of only two functions and two first order derivatives per iteration and the efficiency index of the proposed method is 1.5651. Proposed method has been compared with the methods of Parhi, and Gupta [15] and that of Kou and Li [8]. Method discussed in this paper does not require the evaluation of the second order derivative of the given function as required in the family of Chebyshev–Halley type methods. The efficiency of the method is verified on a number of numerical examples. Method has also been compared with some existing sixth order methods.

    Citing this Journal Article :

    Manoj Kumar Singh, Arvind K. Singh, "A six-order method based on heronian mean for solving non-linear equations", https://www.ijltet.org/journal_details.php?id=921&j_id=3994, Volume 9 Issue 1 - September 2017, 158-165, #ijltetorg