Darvishi, M. T.; Barati, A. A third-order Newton-type method to solve systems of nonlinear equations. (English) Zbl 1116.65060 Appl. Math. Comput. 187, No. 2, 630-635 (2007). Summary: We present a third-order Newton-type method to solve systems of nonlinear equations. In the first part we present theoretical preliminaries of the method. Secondly, we solve some systems of nonlinear equations. All test problems show the third-order convergence of our method. Cited in 2 ReviewsCited in 69 Documents MSC: 65H10 Numerical computation of solutions to systems of equations Keywords:systems of nonlinear equations; Newton-type method; third-order convergence; numerical examples PDF BibTeX XML Cite \textit{M. T. Darvishi} and \textit{A. Barati}, Appl. Math. Comput. 187, No. 2, 630--635 (2007; Zbl 1116.65060) Full Text: DOI OpenURL References: [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] Chun, Ch., A new iterative method for solving nonlinear equations, Appl. math. comput., 178, 2, 415-422, (2006) · Zbl 1105.65057 [3] Chun, Ch., Iterative methods improving newton’s method by the decomposition method, Comput. math. appl., 50, 1559-1568, (2005) · Zbl 1086.65048 [4] 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 [5] Frontini, M.; Sormani, E., Some variants of newton’s method with third-order convergence, Appl. math. comput., 140, 419-426, (2003) · Zbl 1037.65051 [6] Homeier, H.H.H., On Newton-type methods with cubic convergence, J. comput. appl. math., 176, 425-432, (2005) · Zbl 1063.65037 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.