Abstract
Conference Title: 2015 2nd International Conference on Recent Advances in Engineering & Computational Sciences (RAECS) Conference Start Date: 2015, Dec. 21 Conference End Date: 2015, Dec. 22 Conference Location: Chandigarh, India Construction of higher-order two-point and globally convergent methods for computing simple roots of nonlinear equations is one of the earliest and challenging problem of numerical analysis. The principle aim of this manuscript is to propose a new highly efficient two-point family of iterative methods having sixth-order convergence, permitting [function of]'(x) = 0, in the vicinity of the required root. Each member of the proposed scheme is free from second-order derivative. A higher-order family of double-Newton methods with a bivariate weighting function proposed by Guem et. al (2015) is a special case of our proposed scheme. A variety of concrete numerical examples demonstrate that our proposed scheme perform better than existing sixth-order methods available in the literature. In their dynamical study, it has been observed that the proposed methods have better stability and robustness as compared to the other existing methods.