Development of Optimal Eighth Order Derivative-Free Methods for Multiple Roots of Nonlinear Equations
نویسندگان
چکیده
منابع مشابه
THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS
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.
متن کاملNew Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations
A new family of eighth-order derivative-freemethods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight. These new methods are derivative-free and only use four evaluations of the function per iteration. In fact, we have obtained the optimal order of convergence which supports the Kung and Traub conjecture. Kung and Traub conjectured...
متن کاملA Family of Optimal Derivative Free Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations
In this paper, modification of Steffensen’s method with eight-order convergence is presented. We propose a family of optimal three-step methods with eight-order convergence for solving the simple roots of nonlinear equations by using the weight function and interpolation methods. Per iteration this method requires four evaluations of the function which implies that the efficiency index of the d...
متن کاملthird-order and fourth-order iterative methods free from second derivative for finding multiple roots of nonlinear equations
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.
متن کاملNew Families of Fourth-Order Derivative-Free Methods for Solving Nonlinear Equations with Multiple Roots
In this paper, two new fourth-order derivative-free methods for finding multiple zeros of nonlinear equations are presented. In terms of computational cost the family requires three evaluations of functions per iteration. It is proved that the each of the methods has a convergence of order four. In this way it is demonstrated that the proposed class of methods supports the Kung-Traub hypothesis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Symmetry
سال: 2019
ISSN: 2073-8994
DOI: 10.3390/sym11060766