The third order mean-based Jarratt-type method for finding simple roots of nonlinear equation

Abstract

This paper presents a new variant of the third-order iterative scheme for finding a simple root of nonlinear equation. The new scheme is a combination of Jarratt's method and the mean-based Newton's method of the third order. It is numerically compared with several relevant mean-based two-step methods, and the test examples agree with the theoretical analysis.