On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

We consider a system of nonlinear equations . A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

[1]  Jafar Saberi-Nadjafi,et al.  A Hybrid of the Newton-GMRES and Electromagnetic Meta-Heuristic Methods for Solving Systems of Nonlinear Equations , 2009, J. Math. Model. Algorithms.

[2]  Emran Tohidi,et al.  The spectral method for solving systems of Volterra integral equations , 2012 .

[3]  Erhan Turan,et al.  Set Reduction In Nonlinear Equations , 2012, ArXiv.

[4]  Homer F. Walker,et al.  Globally Convergent Inexact Newton Methods , 1994, SIAM J. Optim..

[5]  Wah June Leong,et al.  A Low Memory Solver for Integral Equations of Chandrasekhar Type in the Radiative Transfer Problems , 2011 .

[6]  Z. Bai,et al.  A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations , 2007 .

[7]  Rajni Sharma,et al.  An efficient fourth order weighted-Newton method for systems of nonlinear equations , 2012, Numerical Algorithms.

[8]  Fazlollah Soleymani,et al.  A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals , 2012, Appl. Math. Comput..

[9]  Konstantinos Goulianas,et al.  Finding all roots of 2 × 2 nonlinear algebraic systems using back-propagation neural networks , 2010, Neural Computing and Applications.

[10]  Chang-Hyun Kim,et al.  A comparison of the Newton-Krylov method with high order Newton-like methods to solve nonlinear systems , 2010, Appl. Math. Comput..

[11]  M. Darvishi,et al.  SOME THREE-STEP ITERATIVE METHODS FREE FROM SECOND ORDER DERIVATIVE FOR FINDING SOLUTIONS OF SYSTEMS OF NONLINEAR EQUATIONS , 2009 .

[12]  Mohammad Taghi Darvishi,et al.  HIGH-ORDER NEWTON-KRYLOV METHODS TO SOLVE SYSTEMS OF NONLINEAR EQUATIONS , 2011 .

[13]  Fazlollah Soleymani,et al.  Regarding the accuracy of optimal eighth-order methods , 2011, Math. Comput. Model..

[14]  Miquel Grau-Sánchez,et al.  On the computational efficiency index and some iterative methods for solving systems of nonlinear equations , 2011, J. Comput. Appl. Math..

[15]  Alicia Cordero,et al.  A modified Newton-Jarratt’s composition , 2010, Numerical Algorithms.

[16]  Michael Trott.  The Mathematica GuideBook for Numerics , 2005 .

[17]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[18]  R. D. Murphy,et al.  Iterative solution of nonlinear equations , 1994 .

[19]  Miguel Ángel Hernández,et al.  On Iterative Methods with Accelerated Convergence for Solving Systems of Nonlinear Equations , 2011, J. Optim. Theory Appl..

[20]  Ali Barati,et al.  A note on the local convergence of iterative methods based on Adomian decomposition method and 3-node quadrature rule , 2008, Appl. Math. Comput..

[21]  Stan Wagon.  Mathematica in action , 1991 .