zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Some iterative methods for solving a system of nonlinear equations. (English) Zbl 1165.65349
Summary: We suggest and analyze two new two-step iterative methods for solving the system of nonlinear equations using quadrature formulas. We prove that these new methods have cubic convergence. Several numerical examples are given to illustrate the efficiency and the performance of the new iterative methods. These new iterative methods may be viewed as an extension and generalizations of the existing methods for solving the system of nonlinear equations.
MSC:
65H10Systems of nonlinear equations (numerical methods)
65J15Equations with nonlinear operators (numerical methods)
References:
[1]Burden, R. L.; Faires, J. D.: Numerical analysis, (2001)
[2]Ortega, J. M.; Rheinboldt, W. C.: Iterative solution of nonlinear equations in several variables, (1970) · Zbl 0241.65046
[3]Abbasbandy, S.: Extended Newton’s method for a system of nonlinear equations by modified Adomian decomposition method, Appl. math. Comput. 170, 648-656 (2005) · Zbl 1082.65531 · doi:10.1016/j.amc.2004.12.048
[4]Babolian, E.; Biazar, J.; Vahidi, A. R.: Solution of a system of nonlinear equations by adimian decomposition method, Appl. math. Comput. 150, 847-854 (2004) · Zbl 1075.65073 · doi:10.1016/S0096-3003(03)00313-8
[5]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 · doi:10.1016/j.amc.2006.08.080
[6]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 · doi:10.1016/j.amc.2006.11.022
[7]Golbabai, A.; Javidi, M.: A new family of iterative methods for solving system of nonlinear algebric equations, Appl. math. Comput. 190, 1717-1722 (2007) · Zbl 1227.65046 · doi:10.1016/j.amc.2007.02.055
[8]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, Appl. math. Comput. 200, 452-458 (2008) · Zbl 1160.65018 · doi:10.1016/j.amc.2007.11.009
[9]Cordero, A.; Torregrosa, J. R.: Variants of Newton’s method for functions of several variables, Appl. math. Comput. 183, 199-208 (2006) · Zbl 1123.65042 · doi:10.1016/j.amc.2006.05.062
[10]Cordero, A.; Torregrosa, J. R.: Variants of Newton’s method using fifth-order quadrature formulas, Appl. math. Comput. 190, 686-698 (2007) · Zbl 1122.65350 · doi:10.1016/j.amc.2007.01.062
[11]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 · doi:10.1016/j.amc.2006.09.115
[12]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 · doi:10.1016/S0096-3003(03)00178-4
[13]Atkinson, K. E.: An introduction to numerical analysis, (1987)
[14]Babajee, D. K. R.; Dauhoo, M. Z.: 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 · doi:10.1016/j.amc.2006.05.116
[15]Freudensten, F.; Roth, B.: Numerical solution of systems of nonlinear equations, J. ACM 10, 550-556 (1963) · Zbl 0131.33703 · doi:10.1145/321186.321200
[16]Grau-Sánchez, M.; Peris, J. M.; Gutiérrez, J. M.: Accelerated iterative methods for finding solutions of a system of nonlinear equations, Appl. math. Comput. 190, 1815-1823 (2007) · Zbl 1122.65351 · doi:10.1016/j.amc.2007.02.068
[17]Homeier, H. H. H.: A modified Newton method with cubic convergence: the multivariate case, J. comput. Appl. math. 169, 161-169 (2004) · Zbl 1059.65044 · doi:10.1016/j.cam.2003.12.041
[18]Kou, J.: A third-order modification of Newton method for systems of nonlinear equations, Appl. math. Comput. 191, 117-121 (2007) · Zbl 1193.65077 · doi:10.1016/j.amc.2007.02.030
[19]M. Aslam Noor, Numerical Analysis and Optimization, Lecture Notes, Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan, 2007
[20]Shampine, L. F.; Allen, R. C.; Pruess, S.: Fundamentals of numerical computing, (1997)
[21]Varga, R. S.: Matrix iterative analysis, (2000)
[22]Noor, M. Aslam: Some applications of quadrature formulas for solving nonlinear equations, Nonlinear anal. Forum 12, No. 1, 91-96 (2007) · Zbl 1146.65316
[23]Noor, M. Aslam: Fifth-order convergent iterative method for solving nonlinear equations using quadrature formula, J. math. Control sci. Appl. 1, 241-249 (2007)
[24]Podisuk, M.; Chundang, U.; Sanprasert, W.: Single-step formulas and multi-step formulas of the integration method for solving the initial value problem of ordinary differential equation, Appl. math. Comput. 190, 1438-1444 (2007) · Zbl 1122.65367 · doi:10.1016/j.amc.2007.02.024
[25]Gautschi, W.: Numerical analysis: an introduction, (1997)