New modifications of Hansen–Patrick’s family with optimal fourth and eighth orders of convergence

Munish Kansal, V. Kanwar and Saurabh Bhatia

Applied Mathematics and Computation, 2015, vol. 269, issue C, 507-519

Abstract: In this paper, we present two new second-derivative free classes of iterative methods based on Hansen-Patrick’s family (Hansen and Patrick, 1977 [4]) for solving nonlinear equations numerically. In terms of computational cost, both families require only three and four functional evaluations to achieve optimal fourth and eighth orders of convergence, respectively. Moreover, the local convergence analysis of the proposed methods is also given using hypotheses only on the first derivative and Lipschitz constants. Furthermore, the proposed schemes can also determine the complex zeros without having to start from a complex initial guess as would be necessary with other methods. Numerical examples and comparisons with some existing methods are included to confirm the theoretical results and high computational efficiency.

Keywords: Nonlinear equations; Hansen–Patrick method; Multipoint iterative methods; Kung–Traub conjecture; Computational efficiency (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300315010231
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:269:y:2015:i:c:p:507-519

DOI: 10.1016/j.amc.2015.07.101

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().