×
Babajee, D. K. R.; Dauhoo, M. Z.; Darvishi, M. T.; Barati, A.

A note on the local convergence of iterative methods based on adomian decomposition method and 3-node quadrature rule. (English) Zbl 1160.65018

Appl. Math. Comput. 200, No. 1, 452-458 (2008).
The fourth-order convergence is proved for two Newton type methods, using Ostrowski’s technique based on the point of attraction.
Reviewer: János Karátson (Budapest)

Cited in 1 Review
Cited in 22 Documents

MSC:

65H10 Numerical computation of solutions to systems of equations

Keywords:

fourth-order methods; point of attraction; systems of nonlinear equations; Adomian decomposition method; Newton type method; 3-node quadrature rule
PDF BibTeX XML Cite
\textit{D. K. R. Babajee} et al., Appl. Math. Comput. 200, No. 1, 452--458 (2008; Zbl 1160.65018)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Argyros, I.K., Concerning the “terra incognita” between convergence regions of two Newton methods, Nonlinear anal., 62, 179-184, (2005) · Zbl 1072.65079
[2] M. Drexler, Newton Method as a Global Solver for Non-Linear Problems, Ph.D. Thesis, University of Oxford, 1997.
[3] Guti’errez, J.M.; Hern’andez, M.A., A family of chebyshev – halley type methods in Banach spaces, Bull. austral. math. soc., 55, 113-130, (1997) · Zbl 0893.47043
[4] D.K.R. Babajee, M.Z. Dauhoo, A uni-parametric family of two-point third order iterative methods free from second derivatives: substitute for Chebyshev’s method, J. Comput. Appl. Math., submitted for publication. · Zbl 1123.65036
[5] Frontini, M.; Sormani, E., Third-order methods from quadrature formulae for solving systems of nonlinear equations, Appl. math. comput., 149, 771-782, (2004) · Zbl 1050.65055
[6] Babajee, D.K.R.; Dauhoo, M.Z., An analysis of the properties of the variants of newton’s method with third order convergence, Appl. math. comput., 183, 659-684, (2006) · Zbl 1123.65036
[7] Darvishi, M.T.; Barati, A., Super cubic iterative methods to solve systems of nonlinear equations, Appl. math. comput., 188, 1678-1685, (2007) · Zbl 1119.65045
[8] Darvishi, M.T.; Barati, A., A third-order Newton-type method to solve systems of nonlinear equations, Appl. math. comput., 187, 630-635, (2007) · Zbl 1116.65060
[9] Darvishi, M.T.; Barati, A., A fourth-order method from quadrature formulae to solve systems of nonlinear equations, Appl. math. comput., 188, 257-261, (2007) · Zbl 1118.65045
[10] Adomian, G., Solving frontier problem of physics: the decomposition method, (1994), Kluwer Academic Publishers Dordrecht · Zbl 0802.65122
[11] Ortega, J.M.; Rheinboldt, W.C., Iterative solution of nonlinear equations in several variables, (1970), Academic Press · Zbl 0241.65046
[12] Ostrowski, A., LES points d’attraction et de repulsions pour l’iteration dans l’espace à n dimensions, CR acad. sci. Paris, 244, 288-289, (1957)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.