Applied Science and Computer Mathematics

Class of Sixth Order Modified Newton's Methods for Solving Nonlinear equations

  • By Xiaomeng Wang
  • Applied Science and Computer Mathematics, 2(1) (2021): 28-36

Abstract

Two new classes of three-step Newton’s methods based on power mean Newton’s method have been developed, where two existing numerical methods can be regarded as particular cases of the present method. It is shown that the order of convergence of the proposed methods is six. Also, the efficiency index of the present methods is 1.431 and 1.565 respectively, which are better than Newton’s method (1.414). It is observed that our method takes a smaller number of iterations than Newton’s method. Few sixth order methods are compared with the present method where the numbers of iterations for those methods are either same or more than the present methods. Some examples are given to illustrate the performance of the present methods.