Geodesic
On novel classes of iterative methods for solving nonlinear equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 214-221 
F. Soleymani; B. S. Mousavi. On novel classes of iterative methods for solving nonlinear equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 214-221. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a3/
@article{ZVMMF_2012_52_2_a3,
     author = {F. Soleymani and B. S. Mousavi},
     title = {On novel classes of iterative methods for solving nonlinear equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {214--221},
     year = {2012},
     volume = {52},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a3/}
}
TY  - JOUR
AU  - F. Soleymani
AU  - B. S. Mousavi
TI  - On novel classes of iterative methods for solving nonlinear equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2012
SP  - 214
EP  - 221
VL  - 52
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a3/
LA  - en
ID  - ZVMMF_2012_52_2_a3
ER  - 
%0 Journal Article
%A F. Soleymani
%A B. S. Mousavi
%T On novel classes of iterative methods for solving nonlinear equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2012
%P 214-221
%V 52
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a3/
%G en
%F ZVMMF_2012_52_2_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we establish two new classes of derivative-involved methods for solving single valued nonlinear equations of the form $f(x)=0$. The first contributed two-step class includes two evaluations of the function and one of its first derivative where its error analysis shows a fourth-order convergence. Next, we construct a three-step high-order class of methods including four evaluations per full cycle to achieve the seventh order of convergence. Numerical examples are included to re-verify the theoretical results and moreover put on show the efficiency of the new methods from our classes.

[1] Sauer T., Numerical Analysis, Pearson, Boston, 2006

[2] Noor M.A., Noor K.I., Al–Said E., Waseem M., “Some new iterative methods for fontinear equations”, Math. Probl. Eng., 2010, 198943, 12 pages | MR | Zbl

[3] Kou J., Li Y., Wang X., “Some variants of Ostrowski's method with seventh-order convergence”, J. Comput. Appl. Math., 209 (2007), 153–159 | DOI | MR | Zbl

[4] Cordero A., Hueso E., Martínez E., Torregrosa J.R., “Efficient three-step iterative methods with sixth order convergence for nonlinear equations”, Numer. Algo., 53 (2010), 485–495 | DOI | MR | Zbl

[5] Pavaloiu I., “Bilateral approximations of solutions of equations by order three Steffensen-type methods”, Stud. Univ. Babes-Bolyai, 51 (2006), 105–114 | MR | Zbl

[6] Soleymani F., “Regarding the accuracy of optimal eighth-order methods”, Math. Comput. Modelling, 53 (2011), 1351–1357 | DOI | MR | Zbl

[7] Soleymani F., Sharifi M., “On a class of fifteenth-order iterative formulas for simple roots”, Internat. Electronic J. of Pure and Appl. Math., 3 (2011), 245–252 | MR

[8] Ye Q., Xu X., “A class of Newton-like methods with cobic convergence for nonlinear equations”, Fixed Point Theory, 11 (2010), 161–168 | MR

[9] Traub J.F., Iterative Methods for solution of equations, Prentice-Hall, New Jersey: Englewood Cliffs, 1964 | MR | Zbl

[10] Kung H.T., Traub J.F., “Optimal order of one-point and multipoint iteration”, J. of ACM, 1974, 643–651 | DOI | MR | Zbl

[11] King R., “A family of fourth-order methods for nonlinear equations”, SIAM J. Numer. Analys., 10 (1973), 876–879 | DOI | MR | Zbl