An optimized Chebyshev–Halley type family of multiple solvers: Extensive analysis and applications

Abstract

In this manuscript, we introduce a higher‐order optimal family of Chebyshev–Halley type methods to solve a univariate nonlinear equation having multiple roots. The proposed scheme considers weight functions that are selected adequately to optimize the convergence order and demands only four functional evaluations at each iteration. An extensive convergence analysis is also provided that demonstrates the establishment of eighth‐order convergence of the developed scheme. As a result, the efficiency index of our scheme is optimal according to the Kung–Traub conjecture. Numerical experiments are performed on some real‐life as well as nonlinear academic problems. In addition, the dynamical study of iterative schemes reflects the good overview of their stability, convergence properties, and graphical aspects by drawing attraction basins in the complex plane. Numerical findings indicate that the proposed methods outperform the existing ones with similar characteristics.