Construction of Tri-parametric derivative free fourth order with and without memory iterative method

Volume 9, Issue 4, pp 1410--1423 http://dx.doi.org/10.22436/jnsa.009.04.01

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2123 Downloads
• 3918 Views

Authors

F. Zafar - Centre for Advanced Studies in Pure and Applied Mathematics(CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan. N. Yasmin - Centre for Advanced Studies in Pure and Applied Mathematics(CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan. M. A. Kutbi - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia. M. Zeshan - Centre for Advanced Studies in Pure and Applied Mathematics(CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan.

Abstract

We have given two general methods of converting with derivative two-step methods to without derivative two-step methods. It can also be observed that this conversion not only retain the optimal order of convergence of the two-step methods but the resulting derivative free families of iterative methods are also extendable to with memory class. The with-memory methods show greater acceleration in the order of convergence. In this way, order of convergence is accelerated from 4 to 7.53 at the most. An extensive comparison of our methods is done with the recent methods of respective domain.

Share and Cite

Keywords

• With and without memory methods
• derivative free
• self accelerating parameters
• accelerated order of convergence.

MSC

•  65D05
•  65H05

References

• [1] A. Cordero, J. R. Torregrosa, Low complexity root finding iteration functions with no derivatives of any order of convergence, J. Comput. Appl. Math., 275 (2015), 502-515.


• [2] A. R. Khan, V. Kumar, N. Hussain, Analytical and numerical treatment of Jungck-Type iterative schemes, Appl. Math. Comput., 231 (2014), 521-535.


• [3] R. F. King , A family of fourth order methods for non-linear equations, SIAM J. Numer. Anal., 10 (1973), 876-879.


• [4] H. T. Kung, J. F. Traub , Optimal order of one point and multipoint iteration, J. Assoc. Compute. Math., 21 (1974), 634-651.


• [5] T. Lotfi, F. Soleymani, M. Ghorbanzadeh, P. Assari, On the construction of some tri-parametric iterative methods with memory , Numer. Algor., 2015 (2015), 11 pages.


• [6] J. M. Ortega, W. G. Rheinboldt, Iterative Solutions of Nonlinear Equations in Several Variables, Academic Press, New York (1970)


• [7] F. Soleymani, T. Lotfi, E. Tanakli, F. K. Haghani , Several iterative methods with memory using self accelerator, Appl. Math. Comput., 254 (2015), 452-458.


• [8] J. F. Traub , Iterative Methods for the Solution of Equations, Prentice Hall, New York, USA (1964)


• [9] X. Wang, T. Zhang, Y. Qin, Efficient two-step derivative-free iterative methods with memory and their dynamics, Int. J. Comp. Math., 2015 (2015), 24 pages.


• [10] F. Zafar, N. Hussain, Z. Fatimah, A. Kharal, Optimal sixteenth order convergent method based on Quasi-Hermite interpolation for computing roots, Sci. World J., 2014 (2014), 18 pages.