New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations

• Autorzy: Somayeh Sharifi , Massimiliano Ferrara , Mehdi Salimi , Stefan Siegmund
• Języki publikacji: EN

Abstrakty

EN

In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to [...] 814≈1.682${8^{{\textstyle{1 \over 4}}}} \approx 1.682$. We describe the analysis of the proposed methods along with numerical experiments including comparison with the existing methods. Moreover, the attraction basins of the proposed methods are shown with some comparisons to the other existing methods.

Słowa kluczowe

EN

Multi-point iterative methods; Maheshwari’s method; Kung and Traub’s conjecture; Basin of attraction

Kategorie tematyczne

• 65H05: Single equations
• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 443-451

Daty

wydano

2016-01-01

otrzymano

2016-01-06

zaakceptowano

2016-05-06

online

2016-07-08

Twórcy

autor

Somayeh Sharifi

• MEDAlics, Research Centre at the University Dante Alighieri, Reggio Calabria,

autor

Massimiliano Ferrara

• Department of Law and Economics, University Mediterranea of Reggio Calabria, Italy and CRIOS – Center for Research in Innovation, Organization and Strategy, Department of Management and Technology, Bocconi University, Milano,

autor

Mehdi Salimi

• MEDAlics, Research Centre at the University Dante Alighieri, Reggio Calabria, E-mail: ,
• Center for Dynamics, Department of Mathematics, Technische Universität Dresden,

autor

Stefan Siegmund

• Center for Dynamics, Department of Mathematics, Technische Universität Dresden,

Identyfikatory

DOI

10.1515/math-2016-0041