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An Efficient Family of Traub-Steffensen-Type Methods for Solving Systems of Nonlinear Equations

Janak Raj Sharma, Puneet Gupta
2014 Advances in Numerical Analysis  
Based on Traub-Steffensen method, we present a derivative free three-step family of sixth-order methods for solving systems of nonlinear equations.  ...  The local convergence order of the family is determined using first-order divided difference operator for functions of several variables and direct computation by Taylor's expansion.  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2014/152187 fatcat:sqkycfhbkvfijotokwj7bzvmxm

Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations

Ramandeep Behl, V. Kanwar, Kapil K. Sharma
2012 Journal of Applied Mathematics  
We present another simple way of deriving several iterative methods for solving nonlinear equations numerically.  ...  Further, new classes of third-order multipoint iterative methods free from a second-order derivative are derived by semidiscrete modifications of cubically convergent iterative methods.  ...  contributed to the readability of this paper.  ... 
doi:10.1155/2012/294086 fatcat:ayzi642x4jaghc3gqfv5vxss5i

SOLVING SYSTEM OF NONLINEAR EQUATIONS USING FAMILY OF JARRATT METHODS

Mustafa Q. Khirallah, M.A. Hafiz
2013 International Journal of Differential Equations and Applications  
The aim of this paper is generalization fourth order Jarratt formula iterative methods for solving system of nonlinear equations (SNLE) of n-dimension with n-variables.  ...  These new algorithms may be viewed as an extensions and generalizations of the existing methods for solving the system of nonlinear equations.  ...  Chun [14] proposed a new fourth order optimal root-finding methods for solving nonlinear equations and obtained the classical Jarratt's family of fourth-order methods are as special cases Maheshwari  ... 
doi:10.12732/ijdea.v12i2.931 fatcat:i3bwbeurzzc5xgpnwmak7krhe4

SOLVING SYSTEM OF NONLINEAR EQUATIONS USING FAMILY OF JARRATT METHODS

Mustafa Q. Khirallah, M.A. Hafiz
2013 International Journal of Differential Equations and Applications  
The aim of this paper is generalization fourth order Jarratt formula iterative methods for solving system of nonlinear equations (SNLE) of n-dimension with n-variables.  ...  These new algorithms may be viewed as an extensions and generalizations of the existing methods for solving the system of nonlinear equations.  ...  Chun [14] proposed a new fourth order optimal root-finding methods for solving nonlinear equations and obtained the classical Jarratt's family of fourth-order methods are as special cases Maheshwari  ... 
doi:10.12732/ijdea.v12i1.931 fatcat:ifnmbteyxbdaten43du6bnpdme

Analysis of two Chebyshev-like third order methods free from second derivatives for solving systems of nonlinear equations

D.K.R. Babajee, M.Z. Dauhoo, M.T. Darvishi, A. Karami, A. Barati
2010 Journal of Computational and Applied Mathematics  
order methods free from second derivatives are considered and analyzed for systems of nonlinear equations.  ...  MSC: 65H05 65H10 65D05 41A25 Keywords: Iterative methods Third order convergence Chebyshev's method Systems of nonlinear equations Efficiency index a b s t r a c t In this paper, two Chebyshev-like third  ...  Acknowledgements The authors are grateful to the unknown referees for their valuable comments to improve the paper.  ... 
doi:10.1016/j.cam.2009.09.035 fatcat:ahvepbj6sfaipiwbo2eaqab76q

Page 1406 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
Nonlinear Sci. Numer. Simul. 3 (1998), no. 3, 152-155. Summary: “This article treats mixed finite element methods for nonlinear hyperbolic second-order equations.  ...  of mixed finite element methods for nonlinear hyperbolic equations.  ... 

Higher-Order Derivative-Free Iterative Methods for Solving Nonlinear Equations and Their Basins of Attraction

Jian Li, Xiaomeng Wang, Kalyanasundaram Madhu
2019 Mathematics  
Based on the Steffensen-type method, we develop fourth-, eighth-, and sixteenth-order algorithms for solving one-variable equations.  ...  The new methods are fourth-, eighth-, and sixteenth-order converging and require at each iteration three, four, and five function evaluations, respectively.  ...  Acknowledgments: The authors would like to thank the editors and referees for the valuable comments and for the suggestions to improve the readability of the paper.  ... 
doi:10.3390/math7111052 fatcat:xtt75iyzfbcfra4huwaf7xwogi

Page 3275 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
Summary: “Parametric derivative-free iterative methods of qua- dratic convergence for solving nonlinear equations are discussed in this paper.  ...  method with quadratic convergence of both diameter and point for enclosing simple zeros of nonlinear equations.  ... 

Novel Computational Iterative Methods with Optimal Order for Nonlinear Equations

F. Soleymani
2011 Advances in Numerical Analysis  
This paper contributes a very general class of two-point iterative methods without memory for solving nonlinear equations. The class of methods is developed using weight function approach.  ...  Per iteration, each method of the class includes two evaluations of the function and one of its first-order derivative.  ...  Acknowledgment The author is so much thankful to Sedigheh Faramarzpour for supporting and providing excellent research facilities during the preparation of this paper. 10 Advances in Numerical Analysis  ... 
doi:10.1155/2011/270903 fatcat:6flpmf5bjnghfcihruckcrkhlu

MODIFIED OPTIMAL FAMILIES OF FOURTH-ORDER JARRATT'S METHOD

R. Behl, V. Kanwar, K.K. Sharma
2013 International Journal of Pure and Applied Mathematics  
In this paper, we present a two parameter modified families of Jarratt's method having quartic convergence for computing simple roots of nonlinear equations, permitting f ′ (x) = 0 in the vicinity of the  ...  Jarratt's method and Zhou et al. family of methods [1] for simple roots can be seen as special cases of our proposed scheme.  ...  Acknowledgments Ramandeep Behl acknowledges the financial support of CSIR, New Delhi, India.  ... 
doi:10.12732/ijpam.v84i4.3 fatcat:i2qyh3fjdrhzjj7wyyw7gp2ywi

Page 4259 of Mathematical Reviews Vol. , Issue 83j [page]

1983 Mathematical Reviews  
Authors’ summary: “A family of two-step fourth order methods, which require two function evaluations per step, is derived for y”=f(x,y).  ...  Costabile, F.; Costabile, C. 83j:65073 Two-step fourth order P-stable methods for second order differential equations. BIT 22 (1982), no. 3, 384-386.  ... 

Page 4790 of Mathematical Reviews Vol. , Issue 86j [page]

1986 Mathematical Reviews  
Author summary (translated from the Russian): “We study a difference method for solving the Dirichlet problem for a second- order nonlinear elliptic equation.  ...  The order of accuracy of the finite-difference schemes is estimated, and a numerical method for solving the finite system of equations is developed.  ... 

A Sixth Order Accuracy Solution to a System of Nonlinear Differential Equations with Coupled Compact Method

Don Liu, Qin Chen, Yifan Wang
2013 Journal of Computational Engineering  
Through a special formulation, a system of nonlinear partial differential equations was solved alternately and explicitly in time without linearizing the nonlinearity.  ...  A system of coupled nonlinear partial differential equations with convective and dispersive terms was modified from Boussinesq-type equations.  ...  Anthonio and Hall [23] simulated free surface flows with a high-order compact finite difference method and a fourth order Runge-Kutta method for temporal discretization.  ... 
doi:10.1155/2013/432192 fatcat:k2ql3vh5fngobf334c2nmzenpy

Page 9296 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
hyperbolic equation of second order for potential flows at supersonic speeds.  ...  For simulation of unsteady flows, a standard fourth- order Runge-Kutta method is used for temporal discretization and the velocity-pressure coupling is ensured at each stage also using the matrix-free  ... 

Page 2631 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
Summary: “This paper discusses the nonlinear Galerkin method for the steady state Kuramoto-Sivashinsky (K-S) equation. A con- vergence result and an error estimate are derived for the method.  ...  Hua'| (PRC-SNO; Shanghai) A note of nonlinear Galerkin method for steady state Kuramoto-Sivashinsky equation.  ... 
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