A Quartically Convergent Jarratt-Type Method for Nonlinear System of Equations

In this work, we propose a new fourth-order Jarratt-type method for solving systems of nonlinear equations. The local convergence order of the method is proven analytically. Finally, we validate our results via some numerical experiments including an application to the Chandrashekar integral equations.

[1]  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..

[2]  Fazlollah Soleymani,et al.  Numerical solution of nonlinear systems by a general class of iterative methods with application to nonlinear PDEs , 2013, Numerical Algorithms.

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

[4]  C. Kelley.  Solution of the Chandrasekhar H‐equation by Newton’s Method , 1980 .

[5]  Fazlollah Soleymani,et al.  A three-step iterative method for non-linear systems with sixth order of convergence , 2013, Int. J. Comput. Sci. Math..

[6]  Alicia Cordero,et al.  Numerical Solution of Turbulence Problems by Solving Burgers' Equation , 2015, Algorithms.

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

[8]  Alicia Cordero,et al.  Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension? , 2014, Appl. Math. Comput..

[9]  Fazlollah Soleymani,et al.  Finding the solution of nonlinear equations by a class of optimal methods , 2012, Comput. Math. Appl..

[10]  F. Soleymani,et al.  Finding the Moore–Penrose inverse by a new matrix iteration , 2015 .

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

[12]  Fazlollah Soleymani.  An efficient and stable Newton-type iterative method for computing generalized inverse AT,S(2)$A_{T,S}^{(2)}$ , 2014, Numerical Algorithms.

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

[14]  Fazlollah Soleymani,et al.  Constructing two-step iterative methods with and without memory , 2015 .

[15]  Muhammad Aslam Noor,et al.  Some iterative methods for solving a system of nonlinear equations , 2009, Comput. Math. Appl..