High order iterative methods without derivatives for solving nonlinear equations

Applied Mathematics and Computation

Volumn 186, Issue 2, 2007, Pages 1617-1623

  Feng, Xinlong ^a,b   He, Yinnian ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b XINJIANG UNIVERSITY   (China)

Author keywords

Homotopy perturbation method; Iterative method; Newton method; Nonlinear equation

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENCE EQUATIONS; ITERATIVE METHODS; NEWTON-RAPHSON METHOD; NUMERICAL METHODS; PERTURBATION TECHNIQUES;

HOMOTOPY PERTURBATION METHODS; ITERATIVE FORMULAE; NUMERICAL EXPERIMENTS; THEORETICAL RESULTS;

NONLINEAR EQUATIONS;

EID: 33947613676     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.08.070     Document Type: Article

References (17)

1. Nayfeh A.H. Perturbation Methods (2000), Wiley, New York
2. Ortega J.M., and Rheinboldt W.G. Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press, New York
3. Phillips G.M., and Taylor P.J. Theory and Applications of Numerical Analysis (1973), Academic Press, Inc.
4. Wu X., and Wu H. On a class of quadratic convergence iteration formulae without derivatives. Appl. Math. Comput. 107 (2000) 77-80
5. Zheng Q. Parametric iterative methods of quadratic convergence without the derivative. Math. Numer. Sinica 25 (2003) 107-112
6. Feng X.L., and He Y.N. Parametric iterative methods of second-order for solving nonlinear equation. Appl. Math. Comput. 173 (2006) 1060-1067
7. He J.-H. Newton-like iteration method for solving algebraic equations. Commun. Nonlinear Sci. Numer. Simul. 3 2 (1998) 106-109
8. He J.-H. Comparison of homotopy perturbation method and homotopy analysis method. Appl. Math. Comput. 156 (2004) 527-539
9. He J.-H. Some asymptotic methods for strongly nonlinear equations. Int. J. Modern Phys. B 20 10 (2006) 1141-1199
10. Abbasbandy S. Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method. Appl. Math. Comput. 145 (2003) 887-893
11. Abbasbandy S. Modified homotopy perturbation method for nonlinear equations and comparison with Adomian decomposition method. Appl. Math. Comput. 172 (2006) 431-438
12. Liao S.J. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 147 (2004) 499-513
13. Liao S.J. An approximate solution technique not depending on small parameters: a special example. Int. J. Non-Linear Mech. 30 3 (1995) 371-380
14. Wu T.-M. A study of convergence on the Newton-homotopy continuation method. Appl. Math. Comput. 168 (2005) 1169-1174
15. Wazwaz A.M. A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl. Math. Comput. 111 (2000) 53-69
16. Householder A.S. The Numerical Treatment of a Single Nonlinear Equation (1970), McGraw-Hill, New York
17. Holmes M.H. Introduction to Perturbation Methods (1995), Springer, Berlin