An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros

Abstract

In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one parameter α to achieve the fourth-order of convergence. Initially, the convergence analysis is performed for particular values of multiple roots. Afterward, it concludes in general. Moreover, the effectiveness of the presented methods are certified on some applications of nonlinear equations and compared with the earlier derivative and derivative-free schemes. The obtained results depict better performance than the existing methods.

Keywords

• nonlinear equations
• Kung–Traub conjecture
• multiple roots
• optimal iterative methods
• efficiency index