- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 294086, 22 pages
Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations
1Department of Mathematics, Panjab University, Chandigarh 160 014, India
2University Institute of Engineering and Technology, Panjab University, Chandigarh 160 014, India
Received 25 June 2012; Revised 20 September 2012; Accepted 4 October 2012
Academic Editor: Alicia Cordero
Copyright © 2012 Ramandeep Behl et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- S. Amat, S. Busquier, and J. M. Gutiérrez, “Geometric constructions of iterative functions to solve nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 157, no. 1, pp. 197–205, 2003.
- V. Kanwar, S. Singh, and S. Bakshi, “Simple geometric constructions of quadratically and cubically convergent iterative functions to solve nonlinear equations,” Numerical Algorithms, vol. 47, no. 1, pp. 95–107, 2008.
- J. F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Englewood Cliffs, NJ, USA, 1964.
- J. M. Gutiérrez and M. A. Hernández, “An acceleration of Newton's method: super-Halley method,” Applied Mathematics and Computation, vol. 117, no. 2-3, pp. 223–239, 2001.
- E. Hansen and M. Patrick, “A family of root finding methods,” Numerische Mathematik, vol. 27, no. 3, pp. 257–269, 1976/77.
- A. M. Ostrowski, Solutions of Equations and System of Equations, Academic Press, New York, NY, USA, 1960.
- W. Werner, “Some improvements of classical iterative methods for the solution of nonlinear equations,” in Numerical Solution of Nonlinear Equations, vol. 878 of Lecture Notes in Mathematics, pp. 426–440, Springer, Berlin, Germany, 1981.
- A. M. Ostrowski, Solution of Equations in Euclidean and Banach Spaces, Academic Press, London, UK, 1973.
- L. W. Johnson and R. D. Roiess, Numerical Analysis, Addison-Wesely, Reading, Mass, USA, 1977.
- V. Kanwar, R. Behl, and K. K. Sharma, “Simply constructed family of a Ostrowski's method with optimal order of convergence,” Computers & Mathematics with Applications, vol. 62, no. 11, pp. 4021–4027, 2011.
- R. F. King, “A family of fourth order methods for nonlinear equations,” SIAM Journal on Numerical Analysis, vol. 10, pp. 876–879, 1973.
- F. A. Potra and V. Pták, “Nondiscreate introduction and iterative processes,” in Research Notes in Mathematics, Pitman, Boston, Mass, USA, 1984.
- H. T. Kung and J. F. Traub, “Optimal order of one-point and multipoint iteration,” Journal of the Association for Computing Machinery, vol. 21, pp. 643–651, 1974.
- P. Jarratt, “Some fourth-order multipoint methods for solving equations,” BIT, vol. 9, pp. 434–437, 1965.
- F. Soleymani, “Optimal fourth-order iterative methods free from derivatives,” Miskolc Mathematical Notes, vol. 12, no. 2, pp. 255–264, 2011.
- M. Sharifi, D. K. R. Babajee, and F. Soleymani, “Finding the solution of nonlinear equations by a class of optimal methods,” Computers & Mathematics with Applications, vol. 63, no. 4, pp. 764–774, 2012.
- F. Soleymani, S. K. Khattri, and S. Karimi Vanani, “Two new classes of optimal Jarratt-type fourth-order methods,” Applied Mathematics Letters, vol. 25, no. 5, pp. 847–853, 2012.
- Behzad Ghanbari, “A new general fourth-order family of methods for finding simple roots of nonlinear equations,” Journal of King Saud University-Science, vol. 23, pp. 395–398, 2011.
- E. Schröder, “Über unendlichviele algorithm zur au osung der gleichungen,” Annals of Mathematics, vol. 2, pp. 317–365, 1870.