Variants of Steffensen-secant method and applications

Applied Mathematics and Computation

Volumn 216, Issue 12, 2010, Pages 3486-3496

  Zheng, Quan ^a   Zhao, Peng ^a   Zhang, Li ^a   Ma, Wenchao ^a  

^a NORTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Derivative free; Multiple shooting method; Newton's method; Nonlinear equation; Simple multiple root; Steffensen's method; Super cubic convergence

Indexed keywords

CUBIC CONVERGENCE; DERIVATIVE-FREE; MULTIPLE SHOOTING; NEWTON'S METHOD; NEWTON'S METHODS;

NEWTON-RAPHSON METHOD; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 77953613885     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.04.058     Document Type: Article

References (15)

1. Ortega J.M., and Rheinboldt W.G. Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press, New York
2. Halley E. Methodus nova, Accurata and facillis inveniendi radices aequationum quarumcumque generaliter, sine praevia reductione. Philos. Trans. Roy. Soc. London 18 (1694) 136-148
3. Candela V., and Marquina A. Recurrence relations for rational cubic methods I: the Halley method. Computing 44 (1990) 169-184
4. Gutierrez J.M., and Herandez M.A. A family of Chebyshev-Halley type methods in Banach spaces. Bull. Aust. Math. Soc. 55 (1997) 113-130
5. Traub J.F. Iterative Methods for the Solution of Equations (1964), Prentice-Hall, Englewood Cliffs, New Jersey
6. Amat S., and Busquier S. A two-step Steffensen's method under modified convergence conditions. J. Math. Anal. Appl. 324 (2006) 1084-1092
7. Zheng Q., Wang J., Zhao P., and Zhang L. A Steffensen-like method and its higher-order variants. Appl. Math. Comput. 214 (2009) 10-16
8. Zheng Q., Liu Z., and Bai R. Variations of Steffensen method with cubic convergence. J. Comput. Anal. Appl. 9 (2007) 431-436
9. Zheng Q., Wang C., and Sun G. A kind of Steffensen method and its third-order variant. J. Comput. Anal. Appl. 11 (2009) 234-238
10. Zhang H., Li D.-S., and Liu Y.-Z. A new method of secant-like for nonlinear equations. Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 2923-2927
11. Jain P. Steffensen-type methods for solving nonlinear equations. Appl. Math. Comput. 194 (2007) 527-533
12. Alarcón V., Amat S., Busquier S., and López D.J. A Steffensen's type method in Banach spaces with applications on boundary-value problems. J. Comput. Appl. Math. 216 (2008) 243-250
13. Hernández M.A., and Rubio M.J. The secant method and divided differences Hölder continuous. Appl. Math. Comput. 124 (2001) 137-149
14. Babajee D.K.R., and Dauhoo M.Z. An analysis of the properties of the variants of Newtons method with third-order convergence. Appl. Math. Comput. 183 (2006) 659-684
15. Homeier H.H.H. On Newton-type methods for multiple roots with cubic convergence. J. Comput. Appl. Math. 231 (2009) 249-254