Modified Efficient Families of Two and Three-Step Predictor-Corrector Iterative Methods for Solving Nonlinear Equations

Abstract

In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting near the root. The main advantage of our methods is that they perform better and moreover, have the same efficiency indices as that of existing multipoint iterative methods. Furthermore, the convergence analysis of the new methods is discussed and several examples are given to illustrate their efficiency.

In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting near the root. The main advantage of our methods is that they perform better and moreover, have the same efficiency indices as that of existing multipoint iterative methods. Furthermore, the convergence analysis of the new methods is discussed and several examples are given to illustrate their efficiency.

Keywords

Nonlinear Equations, Iterative Methods, Multipoint Iterative Methods, Newton’s Method, Traub-Ostrowski’s Method, Predictor-Corrector Methods, Order of Convergence

Nonlinear Equations, Iterative Methods, Multipoint Iterative Methods, Newton’s Method, Traub-Ostrowski’s Method, Predictor-Corrector Methods, Order of Convergence

Cite this paper

nullS. Kumar, V. Kanwar and S. Singh, "Modified Efficient Families of Two and Three-Step Predictor-Corrector Iterative Methods for Solving Nonlinear Equations,"*Applied Mathematics*, Vol. 1 No. 3, 2010, pp. 153-158. doi: 10.4236/am.2010.13020.

nullS. Kumar, V. Kanwar and S. Singh, "Modified Efficient Families of Two and Three-Step Predictor-Corrector Iterative Methods for Solving Nonlinear Equations,"

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