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Variational iteration technique for solving nonlinear equations. (English) Zbl 1188.65067
The authors use the variational iteration technique to construct some new iterative methods for solving nonlinear equations.Two auxiliary functions are used. One of them can be regarded as a predictor iterative method and another as a corrector method. The suggested methods are free from higher-order derivatives and therefore can be considered as alternatives to the Newton method.

MSC:
65H05 Numerical computation of solutions to single equations
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[1] Chun, C.: Some variants of Chebshev-Halley method free from second derivative. Appl. Math. Comput. 191, 193–198 (2007) · Zbl 1193.65053
[2] Gautschi, W.: Numerical Analysis: An Introduction. Birkhauser, Basel (1997) · Zbl 0877.65001
[3] He, J.H.: Variational iteration method-a kind of non-linear analytical technique: some examples. Int. J. Nonlinear Mech. 34(4), 699–708 (1999) · Zbl 1342.34005
[4] He, J.H.: Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. 20, 1144–1199 (2006) · Zbl 1102.34039
[5] He, J.H.: Non-perturbative methods for strongly nonlinear problems. Dissertation de-Verlag im Internet, Gmbh, Berlin (2006)
[6] He, J.H.: Variational iteration method-some recent results and new interpretations. J. Comput. Appl. Math. 207, 3–17 (2007) · Zbl 1119.65049
[7] Inokuti, M., Sekine, H., Mura, T.: General use of the Lagrange multipliers in nonlinear mathematical physics. In: Nemat-Nasser, S. (ed.) Variational Methods in Mechanics of Solids, pp. 156–162. Pergamon, Elmsford (1978)
[8] Noor, M.A.: Numerical analysis and optimization. Lecture Notes, Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan (2007–2008) · Zbl 1186.91072
[9] Noor, M.A.: New classes of iterative methods for nonlinear equations. Appl. Math. Comput. 191, 128–131 (2007) · Zbl 1193.65069
[10] Noor, M.A., Noor, K.I.: Iterative schemes for nonlinear equations. Appl. Math. Comput. 183, 774–779 (2006) · Zbl 1113.65051
[11] Noor, K.I., Noor, M.A.: Pridictor-corrector Halley method for nonlinear equations. Appl. Math. Comput. 188, 1587–1591 (2007) · Zbl 1119.65038
[12] Noor, K.I., Noor, M.A.: Iterative methods with fourth-order convergence for nonlinear equations. Appl. Math. Comput. 189, 221–227 (2007) · Zbl 1300.65029
[13] Noor, K.I., Noor, M.A., Momani, S.: Modified Householder iterative for nonlinear equations. Appl. Math. Comput. 190, 1534–1539 (2007) · Zbl 1122.65341
[14] Noor, M.A., Mohyud-Din, S.T.: Variational iteration techniques for solving higher-order boundary value problems. Appl. Math. Comput. 189, 1929–1942 (2007) · Zbl 1122.65374
[15] Traub, J.F.: Iterative Methods for Solution of Equations. Prentice-Hall, New York (1964) · Zbl 0121.11204
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