EFFICIENT OPTIMAL FAMILIES OF HIGHER-ORDER ITERATIVE METHODS WITH LOCAL CONVERGENCE

Applicable Analysis and Discrete Mathematics

article

Ramandeep Behl¹  J. M. Gutierrez²  I. K. Argyros³  A. S. Alshomrani¹ 

[1] Department of Mathematics, King Abdulaziz University;Department of Mathematics and Computer Sciences, University of La Rioja;Department of Mathematics Sciences Lawton, OK 73505, USA Cameron University

关键词: Nonlinear equations;    Newton's method;    Basin of attraction;    Convergence analysis;    Banach space;   

DOI  :  10.2298/AADM190218050B

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

The main aim of this manuscript is to propose two new schemes having threeand four substeps of order eight and sixteen, respectively. Both families areoptimal in the sense to Kung-Traub conjecture. The derivation of them arebased on the weight function approach. In addition, theoretical and computational properties are fully investigated along with two main theoremsdescribing the order of convergence. Further, we also provide the local convergence of them in Banach space setting under weak conditions. From thenumerical experiments, we find that they perform better than the existingones when we checked the performance of them on a concrete variety of nonlinear scalar equations. Finally, we analyze the complex dynamical behaviorof them which also provide a great extent to this.

【 授权许可】

Unknown