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New iterative schemes for nonlinear equations. (English) Zbl 1116.65056
Summary: We suggest and analyze a new iterative method for solving nonlinear equations by using a new decomposition method. We also discuss the convergence criteria of these iterative methods. Several numerical examples are given to illustrate the efficiency and performance of the new methods. These new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations.

65H05Single nonlinear equations (numerical methods)
Full Text: DOI
[1] Abbasbandy, S.: Improving Newton -- raphson method for nonlinear equations by modified Adomian decomposition method. Appl. math. Comput. 145, 887-893 (2003) · Zbl 1032.65048
[2] Adomian, G.: Nonlinear stochastic systems and applications to physics. (1989) · Zbl 0659.93003
[3] Chun, C.: Iterative methods improving Newton’s method by the decomposition method. Comput. math. Appl. 50, 1559-1568 (2005) · Zbl 1086.65048
[4] He, J. H.: A new iterative method for solving algebraic equations. Appl. math. Comput. 135, 81-84 (2005)
[5] Homeier, H. H.: On Newton-type methods with cubic convergence. J. comput. Appl. math. 176, 425-432 (2005) · Zbl 1063.65037
[6] M. Aslam Noor, Numerical Analysis and Optimization, Lecture Notes, COMSATS Institute of Information Technology, Islamabad, Pakistan, 2006.
[7] M. Aslam Noor, K. Inayat Noor, Some iterative schemes for nonlinear equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.05.084.
[8] Luo, X.: A note on the new iteration for solving algebraic equations. Appl. math. Comput. 171, 1177-1183 (2005) · Zbl 1091.65044