Ball Convergence for Steffensen-type Fourth-order Methods

Abstract

We present a local convergence analysis for a family of Steffensen-type fourth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as [1], [5]-[28] using hypotheses up to the fifth derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.

Stability Anomalies of Some Jacobian-Free Iterative Methods of High Order of Convergence

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Study of a High Order Family: Local Convergence and Dynamics

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Interval Methods with Fifth Order of Convergence for Solving Nonlinear Scalar Equations

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