A third-order Newton-type method to solve systems of nonlinear equations

Darvishi, M. T.; Barati, Ali

doi:10.1016/j.amc.2006.08.080

Cited by 150 publications

(110 citation statements)

References 6 publications

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“…We compare the classical Newton's method (NM), the method of Darvishi and Barati (DV, [10]), the method of Aslam Noor and Waseem (AN, [2]), Algorithm 2.1 (MY1) and Algorithm 2.2 (MY2) introduced in this paper. All numeric computations have been carried out in MATLAB 2010b environment, rounding to 16 significant decimal digits.…”

Section: Numerical Resultsmentioning

confidence: 99%

The iterative methods with higher order convergence for solving a system of nonlinear equations

Chen¹,

Qiu²,

Lin³

et al. 2017

J. Nonlinear Sci. Appl.

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Section: Numerical Resultsmentioning

confidence: 99%

The iterative methods with higher order convergence for solving a system of nonlinear equations

Chen¹,

Qiu²,

Lin³

et al. 2017

J. Nonlinear Sci. Appl.

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“…It converges quadratically when an initial guess value (0) x is close to the roots ξ of the system of nonlinear equations. In order to improve the order of convergence, a few two-step variants of Newton's methods with cubic convergence have been proposed in some literature [3][4][5][6][7][8][9] and references therein. S.…”

Section: F Xmentioning

confidence: 99%

A Family Third-order Methods with One Parameter for Solving Systems of Nonlinear Equations and BVP-ODEs

Liu¹,

Zhang²

2017

dtetr

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Abstract. Efficient numerical solutions for systems of nonlinear equations have always appealed greatly to people in scientific computation and engineering fields. And how to make the two iterative approximate values as precise as possible is an important issue in actual computation. In this paper, we use the linear-combination method to construct a family third-order scheme with one parameter for solving systems of nonlinear equations. Their cubic convergence and corresponding error equation are proved theoretically, and numerical examples are demonstrated as well to show the efficiency and feasibility of the suggested iterative methods.

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“…M. Darvishi and A. Barati [6] received a third-order convergence iterative method based on Adomian decomposition method to the systems of nonlinear equations. M. Frontini and E. Sormani [7] presented third-order midpoint-methods using numerical quadrature formula.…”

Section: Introductionmentioning

confidence: 99%

Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs

Liu¹,

Sun²

2016

JAMP

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In this paper, a group of Gauss-Legendre iterative methods with cubic convergence for solving nonlinear systems are proposed. We construct the iterative schemes based on Gauss-Legendre quadrature formula. The cubic convergence and error equation are proved theoretically, and demonstrated numerically. Several numerical examples for solving the system of nonlinear equations and boundary-value problems of nonlinear ordinary differential equations (ODEs) are provided to illustrate the efficiency and performance of the suggested iterative methods.

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A third-order Newton-type method to solve systems of nonlinear equations

Cited by 150 publications

References 6 publications

The iterative methods with higher order convergence for solving a system of nonlinear equations

The iterative methods with higher order convergence for solving a system of nonlinear equations

A Family Third-order Methods with One Parameter for Solving Systems of Nonlinear Equations and BVP-ODEs

Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs

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