[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2012.25.4.669

NOTE ON SOME THIRD-ORDER NONLINEAR SOLVERS FOR THE SOLUTION OF NONLINEAR EQUATIONS

Kim, Weonbae (Department of Mathematics, Daejin University)
Chun, Changbum (Department of Mathematics, Sungkyunkwan University)
Kim, Yong-Il (School of Liberal Arts, Korea University of Technology and Education)

Publication Information

Journal of the Chungcheong Mathematical Society / v.25, no.4, 2012 , pp. 669-676 More about this Journal

Abstract

In this note we extend one well-known iteration formula to derive new third-order methods for solving a nonlinear equation. The comparison with other methods is given.

Keywords

order of convergence; Newton method; iteration functions; nonlinear equations; root-finding methods;

Citations & Related Records

Reference

1	J. F. Traub, Iterative methods for the solution of equations, 2nd Edition, Chelsea publishing company, New York, 1982.
2	J. Kou and Y. Li, A family of new Newton-like methods, Appl. Math. Comput. 192 (2007), 162-167. DOI ScienceOn
3	V. Mamta, V. Kanwar, V.K. Kukreja and S. Singh, On a class of quadratically convergent iteration formulae, Appl. Math. Comput. 166 (2006), 633-637.
4	S.Weerakoon and G.I. Fernando, A variant of Newton's method with accelerated third-order convergence, Appl. Math. Lett. 17 (2000), 87-93.
5	M. Frontini and E. Sormani, Some variants of Newton's method with third-order convergence, J. Comput. Appl. Math. 140 (2003), 419-426. DOI ScienceOn
6	H. H. H. Homeier, On Newton-type methods with cubic convergence, J. Comput. Appl. Math. 176 (2005), 425-432. DOI ScienceOn
7	J. Kou, Y. Li and X. Wang, A modification of Newton method with third-order convergence, Appl. Math. Comput. 181 (2006), 1106-1111. DOI ScienceOn