A new sixth-order Jarratt-type iterative method for systems of nonlinear equations

Yaseen, Saima; Zafar, Fiza

doi:10.1007/s40065-022-00380-2

Cited by 6 publications

(7 citation statements)

References 9 publications

(9 reference statements)

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“…Finally, we discuss the effectiveness of N4 by comparing it in Table 4 with existing family of seventh-order method introduced by: Yaseen et al [27], namely S1 Basins of attraction of all these methods are shown in figures (16)(17)(18)(19)(20). N4 has basins of attraction compatible with S1, S2 and S3 and better in some cases.…”

Section: Seventh Order Methods Comparisonmentioning

confidence: 98%

“…The first approach is based on Halley's method and Taylor's expansion, while the second method employs second derivative approximations to enhance the efficiency of the first method. Many researchers [24][25][26][27][28][29][30] introduced different new two-step, three-step, or four-step iterative methods of higher orders by utilizing different methods.…”

Section: Introductionmentioning

confidence: 99%

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Graphical Insights into Dynamical Behavior: Advanced Iterative Methods for Root Finding in Computational Mathematics

Raza,

Toheed,

Haq

et al. 2024

Preprint

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This paper introduces a novel family of Newton-like iterative methods ranging from fourth to seventh order, specifically designed for the efficient determination of simple roots in nonlinear equations. Outperforming existing methods, our proposed techniques exhibit superior stability and expanded basin sizes. Their unprecedented reliability and broad applicability position them as valuable assets for addressing real-world challenges in diverse domains such as Mathematical Modeling, Biomathematics, and Thermodynamics. To illuminate the dynamic behavior of these methods, we employ the graphical tool 'Basin of Attraction'. Through comprehensive analysis, our research demonstrates a significant enhancement in accuracy and convergence rates, presenting a modest yet impactful contribution to the realm of computational mathematics. Mathematics Subject Classification: 65H04, 65H05

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Section: Seventh Order Methods Comparisonmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Graphical Insights into Dynamical Behavior: Advanced Iterative Methods for Root Finding in Computational Mathematics

Raza,

Toheed,

Haq

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…We developed a new sixth-order method by modifying the second step of the method from [29] for solving nonlinear systems of equations.…”

Section: Development Of Methodsmentioning

confidence: 99%

An Efficient Jarratt-Type Iterative Method for Solving Nonlinear Global Positioning System Problems

Yaseen

Zafar

Alsulami

2023

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The global positioning system (GPS) is a satellite navigation system that determines locations. Whenever the baseline satellites are serviced or deactivated, the Space Force often flies more than 24 GPS satellites to maintain coverage. The additional satellites are not regarded as a part of the core constellation but may improve the performance of the GPS. In this study of GPS models, we solved various problems. We examined each set of four satellites separately. Advancements in computer softwares have made computations much more precise. We can use iterative methods to solve GPS problems. Iterative schemes for solving nonlinear equations have always been of great importance because of their applicability to real-world problems. This paper involves the development of an efficient family of sixth-order Jarratt-type iterative schemes for analyzing nonlinear global positioning systems.

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“…The purpose of presently used method tries to decrease function evaluation costs as much as feasible while enhancing convergence order. Such types of estimations are taken by so many researchers [2,3,6,8,9,11,16,18,21,23]. Hence, after merging Eq n : (8) and Eq n : (9), We acquire the proposed method shown below:…”

Section: Methodsmentioning

confidence: 99%

A Modified Hybrid Method For Solving Non-Linear Equations With Computational Efficiency

Shehzad Ali Soomro,

Asif Ali Shaikh,

Qureshi

et al. 2023

VFAST trans. math.

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This paper proposes a modified hybrid method for solving non-linear equations that improves computational efficiency while maintaining accuracy. The proposed method combines the advantages of the traditional Halley’s and mean-based methods, resulting in a more efficient algorithm. The modified hybrid method starts with Halley’s method and then switches to the mean-based method for rapid convergence. To further improve the efficiency of the algorithm, the proposed method incorporates a dynamic selection criterion to choose the appropriate method at each iteration. Numerical experiments are performed to evaluate the performance of the proposed method in comparison to other existing methods. The results show that the modified hybrid method is computationally efficient and can achieve high accuracy in a shorter time than other commonly used methods having similar features. The proposed method is applicable to a wide range of non-linear equations and can be used in various fields of science and engineering where non-linear equations arise. The modified hybrid method provides an effective tool for solving non-linear equations, offering significant improvements in computational efficiency over existing methods.

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A new sixth-order Jarratt-type iterative method for systems of nonlinear equations

Cited by 6 publications

References 9 publications

Graphical Insights into Dynamical Behavior: Advanced Iterative Methods for Root Finding in Computational Mathematics

Graphical Insights into Dynamical Behavior: Advanced Iterative Methods for Root Finding in Computational Mathematics

An Efficient Jarratt-Type Iterative Method for Solving Nonlinear Global Positioning System Problems

A Modified Hybrid Method For Solving Non-Linear Equations With Computational Efficiency

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