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A study of 3μth-order of convergence of Chebyshev–Halley family method and its convergence plane
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A study of 3μth-order of convergence of Chebyshev–Halley family method and its convergence plane
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Journal Article
A study of 3μth-order of convergence of Chebyshev–Halley family method and its convergence plane
2024
Overview
The main focus of this paper is to study a new type of Caputo fractional Chebyshev–Halley family method (CFCHFM) of order at least 3
μ
to approximate zeros
x
∗
of nonlinear equations. In the present manuscript, we have explained and illustrated the effect of the Caputo-type fractional derivative on the Chebyshev–Halley family of iterative methods in the search for zeros of nonlinear equations using the convergence plane. Here we have analyzed the 3
μ
th order of convergence and efficiency index of the Chebyshev method, Halley method, and super-Halley method using fractional calculus and compared their methods’ performance with the fractional Newton method.
Publisher
Springer International Publishing,Springer Nature B.V
