Some new efficient multipoint iterative methods for solving nonlinear systems of equations

Lotfi, Taher; Bakhtiari, Parisa; Cordero, Alicia; Mahdiani, Katayoun; Torregrosa, Juan R.

doi:10.1080/00207160.2014.946412

Cited by 49 publications

(35 citation statements)

References 23 publications

(27 reference statements)

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“…Assume that x ∈ S =S(α, ) and F (x) is continuous and nonsingular at α, and x (0) close to α. Then, α is a point of attraction of the sequence {x (k) } generated by the Traub-Steffensen-like method (22). Furthermore, the sequence so developed converges locally to α with order at least 5.…”

Section: The Methods and Analysis Of Convergencementioning

confidence: 99%

“…Applying Equations (34), (35) and (38) in the last step of method (22) and then simplifying, we get the error equation…”

Section: The Methods and Analysis Of Convergencementioning

confidence: 99%

“…Computational efficiency of an iterative method for solving F(x) = 0 is calculated by the efficiency index E = p 1/C , (for detail see [21,22]), where p is the order of convergence and C is the total cost of computation. The cost of computation C is measured in terms of the total number of function evaluations per iteration and the number of operations (that means products and quotients) per iteration.…”

Section: Computational Efficiencymentioning

confidence: 99%

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On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems

2019

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We propose a derivative-free iterative method with fifth order of convergence for solving systems of nonlinear equations. The scheme is composed of three steps, of which the first two steps are that of third order Traub-Steffensen-type method and the last is derivative-free modification of Chebyshev’s method. Computational efficiency is examined and comparison between the efficiencies of presented technique with existing techniques is performed. It is proved that, in general, the new method is more efficient. Numerical problems, including those resulting from practical problems viz. integral equations and boundary value problems, are considered to compare the performance of the proposed method with existing methods. Calculation of computational order of convergence shows that the order of convergence of the new method is preserved in all the numerical examples, which is not so in the case of some of the existing higher order methods. Moreover, the numerical results, including the CPU-time consumed in the execution of program, confirm the accurate and efficient behavior of the new technique.

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Section: The Methods and Analysis Of Convergencementioning

confidence: 99%

“…Applying Equations (34), (35) and (38) in the last step of method (22) and then simplifying, we get the error equation…”

Section: The Methods and Analysis Of Convergencementioning

confidence: 99%

Section: Computational Efficiencymentioning

confidence: 99%

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On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems

2019

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“…Next, we consider our schemes, namely, (22), (23), and (24), recalled as (N M1), (N M2), and (N M3), respectively to investigate the computational conduct of them with existing techniques. We contrast them with sixth-order schemes given by Hueso et al [20] and Lotfi et al [21], where out of them we consider the expressions, namely, (14-15) for t 1 = − 9 4 and s 2 = 9 8 and (5), known as (HU) and (LO), respectively. In addition, we also compare them with an Ostrowski-type method proposed by Grau-Sánchez et al [22], where among them we choose the iterative scheme (7), denoted by (GR).…”

Section: Numerical Experimentationmentioning

confidence: 99%

A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems

Behl

Argyros

2020

Mathematics

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Many real-life problems can be reduced to scalar and vectorial nonlinear equations by using mathematical modeling. In this paper, we introduce a new iterative family of the sixth-order for a system of nonlinear equations. In addition, we present analyses of their convergences, as well as the computable radii for the guaranteed convergence of them for Banach space valued operators and error bounds based on the Lipschitz constants. Moreover, we show the applicability of them to some real-life problems, such as kinematic syntheses, Bratu's, Fisher's, boundary value, and Hammerstein integral problems. We finally wind up on the ground of achieved numerical experiments, where they perform better than other competing schemes.

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“…Lotfi et al [17] attempt to put forward a new multipoint iterative method of sixth-order convergence for approximating solutions of nonlinear systems of equations. The authors use it as a predictor to derive a general multipoint method.…”

mentioning

confidence: 99%