A variant of Newton’s method based on Simpson’s three-eighths rule for nonlinear equations

Chen, Jen-Yuan; Kincaid, David R.; Lin, Bei-Ru

doi:10.1016/j.aml.2017.11.014

Cited by 6 publications

(3 citation statements)

References 9 publications

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“…In its development, the researchers have successfully modified Newton method where one of the objectives is to increase the speed of iteration. Among these modifications are the approaches presented by (Weerakoon & Fernando, 2000), (Hansonov et al, 2002), (Chen et al, 2018) etc. Notably, these articles share a common theme of developing iterative methods though the numerical application of the Trapezoidal and Simpson methods.…”

Section: Wherementioning

confidence: 99%

“…However, it is less efficient than MNT because it requires five function evaluations on each iteration so that the efficiency index of this method is 1,246 which is smaller than MTN even Newton. A new variation of the Newton method was developed by (Chen et al, 2018) employing the Simpson 3/8 approximation to calculate the integral area on the equation ( 2) thus obtaining a Newton-Simpson variant of the 3/8 method (MNS8)…”

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confidence: 99%

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Variant of Trapezoidal-Newton Method for Solving Nonlinear Equations and its Dynamics

Putra,

Imran,

Putri

et al. 2023

ijqrm

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This article introduces a novel approach resulting from the adaptation of Trapezoidal-Newton method variants. The iterative process is enhanced through the incorporation of a numerical integral strategy derived from two-partition Trapezoidal method. Through rigorous error analysis, the study establishes a third order convergence for this method. It emerges as a viable alternative for solving nonlinear equations, a conclusion substantiated by computational costs conducted on diverse nonlinear equation forms. Furthermore, an exploration of basin of attraction analyses that this method exhibits faster convergence compared to other Newton-type methods, albeit with a slightly expanded divergent region with a variant of Newton Simpson’s method.

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Section: Wherementioning

confidence: 99%

mentioning

confidence: 99%

Variant of Trapezoidal-Newton Method for Solving Nonlinear Equations and its Dynamics

Putra,

Imran,

Putri

et al. 2023

ijqrm

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“…It is difficult to find a solution that may be complex or long. Therefore, it requires that we resort to numerical computational techniques, and master the test in a number of related numerical tasks [2]. The feature of different answer to the request is based on Simpson's basic principle.…”

Section: Introductionmentioning

confidence: 99%

Applications of Numerical Integrations on the Trapezoidal and Simpson's Methods to Analytical and MATLAB Solutions

Ali¹,

Abbas²

2022

MMEP

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Applied mathematics has become widely used among the computer engineering community and various sciences. Not only that, but accuracy and speed are now required. Numerical methods have been submitted to demonstrate the efficiency and accuracy of these methods by assigning them to a computer that previously been corrected in computer formats. This key feature makes the solution perfect and easy to used Simpson 1/3 and Simpson 3/8 are applied to the proposed equation. A trapezoidal method of fractional differential equations, solved using different numerical methods to demonstrate the accuracy of properties, was used. We dealt with many numerical algorithms. Below are decisions with written and unwritten differential equations. Generate error analysis and stability analysis for a high-resolution digital system. Research objectives: Turns out numerical solutions are very accurate near the exact solution. This paper aims to provide numerical calculations for different methods. The graph is compared with the computer literary graphs for clarity. Effectiveness of numerical algorithms used with exact solutions and profitable MATLAB solutions.

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A multistep Steffensen‐type method for solving nonlinear systems of equations

Amat

Argyros²,

Busquier

et al. 2019

Math Methods in App Sciences

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A variant of Newton’s method based on Simpson’s three-eighths rule for nonlinear equations

Cited by 6 publications

References 9 publications

Variant of Trapezoidal-Newton Method for Solving Nonlinear Equations and its Dynamics

Variant of Trapezoidal-Newton Method for Solving Nonlinear Equations and its Dynamics

Applications of Numerical Integrations on the Trapezoidal and Simpson's Methods to Analytical and MATLAB Solutions

A multistep Steffensen‐type method for solving nonlinear systems of equations

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