Original scientific paper

High-order Newton-type iterative methods with memory for solving nonlinear equations

Xiaofeng Wang ; School of Mathematics and Physics, Bohai University, Liaoning, China
Tie Zhang ; College of Sciences, Northeastern University, Liaoning, China

Abstract

In this paper, we present a new family of two-step Newton-type iterative methods with memory for solving nonlinear equations. In order to obtain a Newton-type method with memory, we first present an optimal two-parameter fourth-order Newton-type method without memory. Then, based on the two-parameter method without memory, we present a new two-parameter Newton-type method with memory. Using two self-correcting parameters calculated by Hermite interpolatory polynomials, the $R$-order of convergence of a new Newton-type method with memory is increased from 4 to 5.7016 without any additional calculations. Numerical comparisons are made with some known methods by using the basins of attraction and through numerical computations to demonstrate the efficiency and the performance of the presented methods.

Keywords

Newton-type iterative method with memory; nonlinear equations; $R-$order convergence; root-finding

Hrčak ID:

121828

URI

https://hrcak.srce.hr/121828

Publication date:

26.5.2014.

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