Novel Computational Iterative Methods with Optimal Order for Nonlinear Equations. (8th December 2011)

• Record Type: Journal Article
• Authors: Soleymani, F.
• Other Names: Benzi Michele Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2011(2011)
• Publication Date: 2011-12-08
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2011/270903
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : This paper contributes a very general class of two-point iterative methods without memory for solving nonlinear equations. The class of methods is developed using weight function approach. Per iteration, each method of the class includes two evaluations of the function and one of its first-order derivative. The analytical study of the main theorem is presented in detail to show the fourth order of convergence. Furthermore, it is discussed that many of the existing fourth-order methods without memory are members from this developed class. Finally, numerical examples are taken into account to manifest the accuracy of the derived methods.