title: Optimal sixteenth order convergent method based on quasi-Hermite interpolation for computing roots.
abstract: We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton's method is also used for finding the enough accurate initial approximations. Some figures show the enclosure of finitely many zeroes of nonlinear equations in an interval. Basins of attractions show the effectiveness of the method.
authors.affiliation: Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan.
authors.forename: Fiza
authors.identifier: 0000-0003-0552-2783
authors.initials: F
authors.lastname: Zafar
authors.affiliation: Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
authors.forename: Nawab
authors.initials: N
authors.lastname: Hussain
authors.affiliation: Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan.
authors.forename: Zirwah
authors.initials: Z
authors.lastname: Fatimah
authors.affiliation: National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan.
authors.forename: Athar
authors.identifier: 0000-0002-7540-3424
authors.initials: A
authors.lastname: Kharal
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008433:Mathematics / Q000379:methods*; D008962:Models, Theoretical