Highly efficient family of iterative methods for solving nonlinear models

Behl, Ramandeep; Sarría, Íñigo; González, Rubén; Magreñán, Á. Alberto

doi:10.1016/j.cam.2018.06.042

Cited by 33 publications

(25 citation statements)

References 19 publications

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“…with the efficiency index 1.495. We propose the following modification in the interval form for (12). We seek a solution of the equation f (x) = 0, on the interval x = [x, x].…”

Section: Second Methods Of Kou In Classic and Interval Formmentioning

confidence: 99%

“…Several iterative methods are used to solve nonlinear equations, the most famous being Newton's method. To improve the order of convergence, many authors have proposed modifications to the Newton formula, obtained by various techniques and with different order of convergence [1][2][3][4][5][6][7][8][9] and references related to higher-order iterative methods [10][11][12]. In addition to the classic iteration schemes, interval methods are also used to solve nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Interval Methods with Fifth Order of Convergence for Solving Nonlinear Scalar Equations

Ivanov

Mateva

2019

Axioms

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In this paper, based on Kou’s classical iterative methods with fifth-order of convergence, we propose new interval iterative methods for computing a real root of the nonlinear scalar equations. Some numerical experiments have executed with the program INTLAB in order to confirm the theoretical results. The computational results have described and compared with Newton’s interval method, Ostrowski’s interval method and Ostrowski’s modified interval method. We conclude that the proposed interval schemes are effective and they are comparable to the classical interval methods.

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“…with the efficiency index 1.495. We propose the following modification in the interval form for (12). We seek a solution of the equation f (x) = 0, on the interval x = [x, x].…”

Section: Second Methods Of Kou In Classic and Interval Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interval Methods with Fifth Order of Convergence for Solving Nonlinear Scalar Equations

Ivanov

Mateva

2019

Axioms

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show abstract

“…The fourth class of iterative methods is of Jarrat-type (B6) and was introduced by R. Behl et al in [26] as…”

Section: Introductionmentioning

confidence: 99%

A New Three-Step Class of Iterative Methods for Solving Nonlinear Systems

2019

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In this work, a new class of iterative methods for solving nonlinear equations is presented and also its extension for nonlinear systems of equations. This family is developed by using a scalar and matrix weight function procedure, respectively, getting sixth-order of convergence in both cases. Several numerical examples are given to illustrate the efficiency and performance of the proposed methods.

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“…Mathematics is always changing and the way we teach it also changes as it is presented in [1,2]. In the literature [3][4][5][6][7][8], we can find many problems in engineering and applied sciences that can be solved by finding solutions of equations in a way such as (1). Finding exact solutions for this type of equation is not easy.…”

Section: Introductionmentioning

confidence: 99%

Study of a High Order Family: Local Convergence and Dynamics

et al. 2019

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The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a center-Lipschitz condition where the ball radii are greater than previous studies. We investigate the dynamics of the method. To validate the theoretical results obtained, a real-world application related to chemistry is provided.

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Highly efficient family of iterative methods for solving nonlinear models

Cited by 33 publications

References 19 publications

Interval Methods with Fifth Order of Convergence for Solving Nonlinear Scalar Equations

Interval Methods with Fifth Order of Convergence for Solving Nonlinear Scalar Equations

A New Three-Step Class of Iterative Methods for Solving Nonlinear Systems

Study of a High Order Family: Local Convergence and Dynamics

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