Second derivative free sixth order continuation method for solving nonlinear equations with applications

Prashanth, M.; Magreñán, Á. Alberto; Motsa, S. S.; Sarría, Íñigo

doi:10.1007/s10910-018-0868-7

Cited by 9 publications

(11 citation statements)

References 17 publications

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“…Example 6. Next, we consider the study of the multi-factor effect in which the trajectory of an electron in the air gap between two parallel plates [30] is defined as:…”

Section: Examplementioning

confidence: 99%

One Parameter Optimal Derivative-Free Family to Find the Multiple Roots of Algebraic Nonlinear Equations

et al. 2020

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In this study, we construct the one parameter optimal derivative-free iterative family to find the multiple roots of an algebraic nonlinear function. Many researchers developed the higher order iterative techniques by the use of the new function evaluation or the first-order or second-order derivative of functions to evaluate the multiple roots of a nonlinear equation. However, the evaluation of the derivative at each iteration is a cumbersome task. With this motivation, we design the second-order family without the utilization of the derivative of a function and without the evaluation of the new function. The proposed family is optimal as it satisfies the convergence order of Kung and Traub’s conjecture. Here, we use one parameter a for the construction of the scheme, and for a=1, the modified Traub method is its a special case. The order of convergence is analyzed by Taylor’s series expansion. Further, the efficiency of the suggested family is explored with some numerical tests. The obtained results are found to be more efficient than earlier schemes. Moreover, the basin of attraction of the proposed and earlier schemes is also analyzed.

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“…Example 6. Next, we consider the study of the multi-factor effect in which the trajectory of an electron in the air gap between two parallel plates [30] is defined as:…”

Section: Examplementioning

confidence: 99%

One Parameter Optimal Derivative-Free Family to Find the Multiple Roots of Algebraic Nonlinear Equations

et al. 2020

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“…We consider the Planck's radiation law problem given in [1]. "This problem deals with the calculation of the energy density within an isothermal blackbody and is given by: 5 8 ( ) ,…”

Section: Numerical Applicationsmentioning

confidence: 99%

“…In the course of recent years, numerous researchers have endeavored to develop higher order convergent iterative schemes to solve nonlinear equations f (x) = 0 (1) where f : D ⊆ R → R be a sufficiently differentiable nonlinear function on an open interval D. One of the most frequently used parametric iterative schemes for solving nonlinear equations is Chebyshev-Halley's method. These methods are cubically convergent.…”

Section: Introductionmentioning

confidence: 99%

“…Due to the greater efficiency of computation, the second order Newton's method [11] is also widely used to solve nonlinear equations in R. In addition, construction of multi-point higher order schemes becomes important and more popular due to the improvement in digital computers and symbolic computing. In the most recent decade, numerous researchers around the world have studied multi-point iterative schemes [1][2] with their convergence and complex dynamical properties.…”

Section: Introductionmentioning

confidence: 99%

“…We discuss several applications such as Max Planck's conservative law, chemical equilibrium, and multi-factor effect to demonstrate the productiveness and capability of the suggested method (for γ = 3 2 ). At every iteration our method is compared with Maroju et al method [1] and Parhi and Gupta method [2] in terms of the values | f (x n )| and |x n − x n−1 |. From the numerical experiments, the advantages of our method are observed.…”

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confidence: 99%

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A New Class of Fifth and Sixth Order Root-Finding Methods with Its Dynamics and Applications

Sharma

Parhi

Sunanda

2020

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In this paper, we deal with the construction, analysis and applications of a modified uniparametric family of methods to solve nonlinear equations in R. We study the convergence of new methods which shows the order of convergence is at least five and for a particular value 3/2 of the parameter γ, the method is sixth order convergent. We discuss several applications such as Max Planck’s conservative law, chemical equilibrium and multi-factor effect to demonstrate the productiveness and capability of the suggested method (for γ = 3/2 ). At every iteration our method is compared with Maroju et al. method[1] and Parhi and Gupta method[2] in terms of the values |f (xn)| and |xn − xn−1|. From the numerical experiments, advantages of our method is observed. Furthermore, we study the complex dynamics to determine the stability and dynamical properties of the methods.

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A study on the local convergence and complex dynamics of Kou’s family of iterative methods

Argyros

Sharma

Parhi

et al. 2021

SeMA

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Second derivative free sixth order continuation method for solving nonlinear equations with applications

Cited by 9 publications

References 17 publications

One Parameter Optimal Derivative-Free Family to Find the Multiple Roots of Algebraic Nonlinear Equations

One Parameter Optimal Derivative-Free Family to Find the Multiple Roots of Algebraic Nonlinear Equations

A New Class of Fifth and Sixth Order Root-Finding Methods with Its Dynamics and Applications

A study on the local convergence and complex dynamics of Kou’s family of iterative methods

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