Extended iterative schemes based on decomposition for nonlinear models

Argyros, Ioannis K.; Sharma, Debasis; Argyros, Christopher I.; Parhi, Sanjaya Kumar; Sunanda, Shanta Kumari

doi:10.1007/s12190-021-01570-5

Cited by 8 publications

(2 citation statements)

References 29 publications

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“…The study of local and semi-local analysis of an iterative formula allows to estimate the convergence balls, bounds on error and uniqueness region for a solution. The results of local and semi-local convergence of efficient iterative procedures have been deduced in [2,3,[5][6][7]11]. In these works, important results containing convergence radii, measurements on error estimates and expanded utility of these iterative approaches have been given.…”

Section: Introductionmentioning

confidence: 99%

On the semi-local convergence of a sixth order method in Banach space

Argyros¹,

John²,

Jayaraman³

2022

J. Numer. Anal. Approx. Theory

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High convergence order methods are important in computational mathematics, since they generate sequences converging to a solution of a non-linear equation. The derivation of the order requires Taylor series expansions and the existence of derivatives not appearing on the method. Therefore, these results cannot assure the convergence of the method in those cases when such high order derivatives do not exist. But, the method may converge. In this article, a process is introduced by which the semi-local convergence analysis of a sixth order method is obtained using only information from the operators on the method. Numerical examples are included to complement the theory.

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Section: Introductionmentioning

confidence: 99%

On the semi-local convergence of a sixth order method in Banach space

Argyros¹,

John²,

Jayaraman³

2022

J. Numer. Anal. Approx. Theory

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“…Additional studies on Jarratt-like and other iterative processes with their dynamics and convergence are available in [4,8,10,19,20,22,24,28,32].…”

Section: Introductionmentioning

confidence: 99%

Extended three step sixth order Jarratt-like methods under generalized conditions for nonlinear equations

et al. 2022

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The convergence balls as well as the dynamical characteristics of two sixth order Jarratt-like methods (JLM1 and JLM2) are compared. First, the ball analysis theorems for these algorithms are proved by applying generalized Lipschitz conditions on derivative of the first order. As a result, significant information on the radii of convergence and the regions of uniqueness for the solution are found along with calculable error distances. Also, the scope of utilization of these algorithms is extended. Then, we compare the dynamical properties, using the attraction basin approach, of these iterative schemes. At the end, standard application problems are considered to demonstrate the efficacy of our theoretical findings on ball convergence. For these problems, the convergence balls are computed and compared. From these comparisons, it is confirmed that JLM1 has the bigger convergence balls than JLM2. Also, the attraction basins for JLM1 are larger in comparison to JLM2. Thus, for numerical applications, JLM1 is better than JLM2.

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Advancing convergence analysis: extending the scope of a sixth order method

John,

Jayaraman

2024

Indian J Pure Appl Math

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Extended iterative schemes based on decomposition for nonlinear models

Cited by 8 publications

References 29 publications

On the semi-local convergence of a sixth order method in Banach space

On the semi-local convergence of a sixth order method in Banach space

Extended three step sixth order Jarratt-like methods under generalized conditions for nonlinear equations

Advancing convergence analysis: extending the scope of a sixth order method

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