A Novel n-Point Newton-Type Root-Finding Method of High Computational Efficiency

Abstract

A novel Newton-type n-point iterative method with memory is proposed for solving nonlinear equations, which is constructed by the Hermite interpolation. The proposed iterative method with memory reaches the order (2n+2n−1−1+22n+1+22n−2+2n+1)/2 by using n variable parameters. The computational efficiency of the proposed method is higher than that of the existing Newton-type methods with and without memory. To observe the stability of the proposed method, some complex functions are considered under basins of attraction. Basins of attraction show that the proposed method has better stability and requires a lesser number of iterations than various well-known methods. The numerical results support the theoretical results.