A Few Iterative Methods by Using [1, n ]-Order Padé Approximation of Function and the Improvements

Shengfeng Li, Xiaobin Liu and Xiaofang Zhang
Additional contact information
Shengfeng Li: Institute of Applied Mathematics, Bengbu University, Bengbu 233030, China
Xiaobin Liu: School of Computer Engineering, Bengbu University, Bengbu 233030, China
Xiaofang Zhang: Institute of Applied Mathematics, Bengbu University, Bengbu 233030, China

Mathematics, 2019, vol. 7, issue 1, 1-14

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.

Keywords: nonlinear equations; Padé approximation; iterative method; order of convergence; numerical experiment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/1/55/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/1/55/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:1:p:55-:d:195471

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().