Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices. (3rd September 2014)

• Record Type: Journal Article
• Authors: Lotfi, T.; Soleymani, F.; Noori, Z.; Kılıçman, A.; Khaksar Haghani, F.
• Other Names: Ciepliński Krzysztof Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2014(2014)
• Publication Date: 2014-09-03
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2014/912796
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : Two families of derivative-free methods without memory for approximating a simple zero of a nonlinear equation are presented. The proposed schemes have an accelerator parameter with the property that it can increase the convergence rate without any new functional evaluations. In this way, we construct a method with memory that increases considerably efficiency index from 8 1 / 4 ≈ 1.681 to 1 2 1 / 4 ≈ 1.861 . Numerical examples and comparison with the existing methods are included to confirm theoretical results and high computational efficiency.