On a Novel Fourth-Order Algorithm for Solving Systems of Nonlinear Equations

This paper focuses on solving systems of nonlinear equations numerically. We propose an efficient iterative scheme including two steps and fourth order of convergence. The proposed method does not require the evaluation of second or higher order Frechet derivatives per iteration to proceed and reach fourth order of convergence. Finally, numerical results illustrate the efficiency of the method.

[1]  Haijun Wang,et al.  New third-order method for solving systems of nonlinear equations , 2009, Numer. Algorithms.

[2]  Fazlollah Soleymani,et al.  Two new classes of optimal Jarratt-type fourth-order methods , 2012, Appl. Math. Lett..

[3]  Ali Barati,et al.  Analysis of two Chebyshev-like third order methods free from second derivatives for solving systems of nonlinear equations , 2010, J. Comput. Appl. Math..

[4]  Ali Barati,et al.  A fourth-order method from quadrature formulae to solve systems of nonlinear equations , 2007, Appl. Math. Comput..

[5]  M. Frontini,et al.  Third-order methods from quadrature formulae for solving systems of nonlinear equations , 2004, Appl. Math. Comput..

[6]  J. Craggs.  Applied Mathematical Sciences , 1973 .

[7]  Alicia Cordero,et al.  Accelerated methods of order 2p for systems of nonlinear equations , 2010, J. Comput. Appl. Math..

[8]  J. Traub.  Iterative Methods for the Solution of Equations , 1982 .

[9]  Wah June Leong,et al.  An Efficient Solver for Systems of Nonlinear Equations with Singular Jacobian via Diagonal Updating , 2010 .

[10]  Alicia Cordero,et al.  Variants of Newton's Method using fifth-order quadrature formulas , 2007, Appl. Math. Comput..

[11]  Zhonggang Zeng,et al.  Multiple zeros of nonlinear systems , 2011, Math. Comput..

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

[13]  Muhammad Aslam Noor,et al.  Variational iteration technique for solving a system of nonlinear equations , 2013, Optim. Lett..