A few iterative methods by using [1, n]-order Padé approximation of function and the improvements

2Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

Abstract

In this paper, a few single-step iterative methods, including classical Newton's method and Halley's method, are suggested by applying [1, n]-order Padé approximation of function for finding the roots of nonlinear equations at first. In order to avoid the operation of high-order derivatives of function, we modify the presented methods with fourth-order convergence by using the approximants of the second derivative and third derivative, respectively. Thus, several modified two-step iterative methods are obtained for solving nonlinear equations, and the convergence of the variants is then analyzed that they are of the fourth-order convergence. Finally, numerical experiments are given to illustrate the practicability of the suggested variants. Henceforth, the variants with fourth-order convergence have been considered as the imperative improvements to find the roots of nonlinear equations.

Cite

CITATION STYLE

APA

Li, S., Liu, X., & Zhang, X. (2019). A few iterative methods by using [1, n]-order Padé approximation of function and the improvements. Mathematics, 7(1). https://doi.org/10.3390/math7010055

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free