Two new three-step predictor-corrector methods with fifth-order convergence for solving nonlinear equations

Author

Hu, Yunhong ; Fang, Liang ; He, Guoping

Author_Institution

Coll. of Inf. Sci. & Eng., Shandong Univ. of Sci. & Technol., Qingdao, China

Volume

2

fYear

2010

fDate

13-14 Sept. 2010

Firstpage

16

Lastpage

19

Abstract

In this paper, we present two new three-step predictor-corrector methods for solving nonlinear equations. This two algorithms are free from second derivative and per iteration they only require three evaluations of the given function and one evaluation of its first derivative. Convergence analysis shows that they are fifth-order convergent. Numerical tests demonstrate that both of the two new methods are more efficient and more practical than most of known variants of two-step methods.

Keywords

convergence of numerical methods; nonlinear equations; predictor-corrector methods; convergence analysis; fifth order convergence; nonlinear equations; three step predictor corrector method; Convergence; Iterative methods; Newton method; Nonlinear equations; Prediction algorithms; Newton´s method; nonlinear equations; predictor-corrector type iterative method; three-step method; two-step method;

fLanguage

English

Publisher

ieee

Conference_Titel

Computational Intelligence and Natural Computing Proceedings (CINC), 2010 Second International Conference on

Conference_Location

Wuhan

Print_ISBN

978-1-4244-7705-0

Type

conf

DOI

10.1109/CINC.2010.5643799

Filename

5643799