On a general efficient class of four-step root-finding methods

International Journal of Mathematics and Computers in Simulation

Volumn 5, Issue 3, 2011, Pages 181-189

  Soleymani, Fazlollah ^a   Sharifi, Mahdi ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Efficiency index; Error equation; Four step methods; Iterative schemes; Multi point methods; Nonlinear equations; Optimality; Order of convergence; Simple root

Indexed keywords

EID: 79960088356     PISSN: 19980159     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. M. Allame, N. Azad, A new method for solving nonlinear equations by Taylor expansion, in''Applications of Mathematics and Computer Engineering'', Included in ISI/SCI Web of Science and Web of Knowledge, Mexico, (2011), 65-67.
2. A. Cordero, J.L. Hueso, E. Martinez, J.R. Torregrosa, New modifications of Potra-Ptak's method with optimal fourth and eighth orders of convergence, J. Comput. Appl. Math., In Press.
3. A. Cordero, J.L. Hueso, E. Martinez, J.R. Torregrosa, A family of iterative methods with sixth and seventh order convergence for nonlinear equations, Math. Comput. Modelling, 52 (2010), 1490-1496.
4. Y.H. Geum, Y.I. Kim, A penta-parametric family of fifteenth-order multipoint methods for nonlinear equations, Appl. Math. Comput., 217 (2010), 2311-2319.
5. A. Iliev, N. Kyurkchiev, Nontrivial Methods in Numerical Analysis: Selected Topics in Numerical Analysis, LAP LAMBERT Academic Publishing, 2010.
6. J. Kou, Y. Li, A variant of Chebyshev's method with sixth-order convergence, Numer. Algorithms, 43 (2006), 273-278.
7. H.T. Kung, J.F. Traub, Optimal order of one-point and multipoint iteration, J. Assoc. Comput. Mach., 21 (1974), 643-651.
8. N.E. Mastorakis, Solving non-linear equations via genetic algorithms, Proceedings of the 6th WSEAS international conference on Evolutionary computing World Scientific and Engineering Academy and Society (WSEAS) Stevens Point, Wisconsin, USA (2005), ISBN: 960-8457- 26-2.
9. N. Mastorakis, O. Martin, About the numerical solution of a stationary transport equation, Proceedings of the 5th WSEAS Int. Conf. on Simulation, Modeling and Optimization, Corfu, Greece, (2005), 419-426.
10. B. Neta, M.S. Petkovic, Construction of optimal order nonlinear solvers using inverse interpolation, Appl. Math. Comput., In Press.
11. B. Neta, On a family of multipoint methods for non-linear equations, Int. J. Comput. Math., 9 (1981), 353-361.
12. L.D. Petkovic, M.S. Petkovic, J. Dzuniz, A class of three-point rootsolvers of optimal order of convergence, Appl. Math. Comput., 216 (2010), 671-676.
13. M.S. Petkovic, On a general class of multipoint root-finding methods of high computational efficiency, SIAM J. Numer. Anal. In Press.
14. P. Sargolzaei, F. Soleymani, Accurate fourteenth-order methods for solving nonlinear equations, Numer. Algorithms, (2011). doi: 10.1007/s11075-011-9467-4.
15. J.R. Sharma, R. Sharma, A new family of modified Ostrowski's methods with accelerated eighth order convergence, Numer. Algorithms, 54 (2010), 445-458.
16. F. Soleymani, Concerning some sixth-order iterative methods for finding the simple roots of nonlinear equations, Bull. Math. Anal. Appl., 2 (2010), 146-151.
17. F. Soleymani, Revisit of Jarratt method for solving nonlinear equations, Numer. Algorithms, 57 (2011), 377-388.
18. F. Soleymani, V. Hosseniabadi, New third- and sixth-order derivativefree techniques for nonlinear equations, J. Math. Research, 3 (2011), 107-112.
19. F. Soleimani, F. Soleymani, Computing simple roots by a sixth-order iterative method, Int. J. Pure Appl. Math., 69 (2011), 41-48.
20. F. Soleymani, Regarding the accuracy of optimal eighth-order methods, Math. Comput. Modelling, 53 (2011), 1351-1357.
21. http://en.wikipedia.org/wiki/Newton'smethod.
22. P. Wang, A third-order family of Newton-like iteration methods for solving nonlinear equations, J. Numer. Math. Stoch., 3 (2011), 13-19.
23. X. Wang, L. Liu, New eighth-order iterative methods for solving nonlinear equations, J. Comput. Appl. Math., 234 (2010), 1611-1620.
24. Y. Wu, K.F. Cheung, Two-parameter homotopy method for nonlinear equations, Numer. Algorithms, 53 (2010), 555-572.
25. B.I. Yun, A non-iterative method for solving non-linear equations, Appl. Math. Comput., 198 (2008), 458-467.
26. D. Zaharieva, N. Kyurkchiev, A. Iliev, On a method for solving some special classes of nonlinear systems of equations, Int. J. Pure Appl. Math., 69 (2011), 117-124.
27. B. Zheng, Exact solutions for two non-linear equations, WSEAS Trans. Math., 9 (2010), 691-699.