On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence
نویسندگان
چکیده
منابع مشابه
Optimal eighth-order simple root-finders free from derivative
The calculation of derivatives of a function mostly takes up a great deal of time and even in some cases, such as the existing problems in engineering and optimization, is impossible to be evaluated directly. Accordingly, an accurate derivative-free class of three-step methods is suggested for solving ( ) = 0. The proposed three-step technique comprises four evaluations of the function per iter...
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A class of three-step eighth-order root solvers is constructed in this study. Our aim is fulfilled by using an interpolatory rational function in the third step of a three-step cycle. Each method of the class reaches the optimal efficiency index according to the Kung-Traub conjecture concerning multipoint iterative methods without memory. Moreover, the class is free from derivative calculation ...
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In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.
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In this paper new fourth order optimal root-finding methods for solving nonlinear equations are proposed. The classical Jarratt’s family of fourth-order methods are obtained as special cases. We then present results which describe the conjugacy classes and dynamics of the presented optimal method for complex polynomials of degree two and three. The basins of attraction of existing optimal metho...
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ژورنال
عنوان ژورنال: Mathematics
سال: 2020
ISSN: 2227-7390
DOI: 10.3390/math8071091