A study of the local convergence of a fifth order iterative method

Singh, Sukjith; Martínez, Eulalia; Prashanth, M.; Behl, Ramandeep

doi:10.1007/s13226-020-0409-5

Cited by 24 publications

(11 citation statements)

References 17 publications

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“…There are no uniqueness of χ * results or error bounds on ||x t − x * ||, ||y t − x t ||, ||x t+1 − y t || that can be computed. The same observations can be made for the local results of other methods [4,[6][7][8][9]. Hence, there is a need to develop results using conditions only on the first derivative that appears on these methods.…”

Section: Introductionmentioning

confidence: 77%

On the Semi-Local Convergence of a Noor–Waseem-like Method for Nonlinear Equations

et al. 2022

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The significant feature of this paper is that the semi-local convergence of high order methods for solving nonlinear equations defined on abstract spaces has not been studied extensively as done for the local convergence by a plethora of authors which is certainly a more interesting case. A process is developed based on majorizing sequences and the notion of restricted Lipschitz condition to provide a semi-local convergence analysis for the third convergent order Noor–Waseem method. Due to the generality of our technique, it can be used on other high order methods. The convergence analysis is enhanced. Numerical applications complete are used to test the convergence criteria.

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Section: Introductionmentioning

confidence: 77%

On the Semi-Local Convergence of a Noor–Waseem-like Method for Nonlinear Equations

et al. 2022

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“…However, NI may be convergent (see the numerical Section, Example 4.1). That is why these criteria are weakened in [2][3][4]. But no new conditions are added.…”

Section: Nonlinear Equationmentioning

confidence: 99%

“…That is no additional effort is needed. The generality of this idea allows its application on other processes [3,4,11].…”

Section: Nonlinear Equationmentioning

confidence: 99%

Updated and Weaker Convergence Criteria of Newton Iterates for Equations

Regmi

Argyros

George

et al. 2022

Eur. J. Math. Anal.

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Newton iteration is often used as a solver for nonlinear equations in abstract spaces. Some of the main concerns are general: Criteria for convergence, error estimations on consecutive iterates, and the location of a solution. A plethora of authors has addressed these concerns by presenting results based on the celebrated Kantorovich theory. This article contributes in this direction by extending earlier results but without additional conditions. These extensions become possible using a more precise majorization than the one given in earlier articles. Numerical experimentation complements the theoretical results involving a partial differential and an integral equation.

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“…Films developed were also found to be flexible leading to a shielding effectiveness (SE) of 20 dB. [ 9 ] Mc Clory et al [ 10 ] studied the electrical and rheological properties of PMMA/MWCNT composites using four types of MWCNT with varied aspect ratio and surface functionalization. The smaller sized nanotubes with higher purity were found to have lower percolation threshold.…”

Section: Introductionmentioning

confidence: 99%

Polymethyl methacrylate reinforced with nickel coated multi‐walled carbon nanotubes: Flame, electrical and mechanical properties

2020

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Composites of polymethyl methacrylate (PMMA) as matrix and nickel‐coated multi‐walled carbon nanotubes (Ni‐MWCNT) as nanofillers were prepared using a melt mixing process. In order to improve the dispersion of the nanofillers in the PMMA matrix and thus enhance matrix‐filler interactions, Ni‐MWCNT was treated with amino propyl triethoxy‐silane (APTS). The shielding effectiveness (SE) of the composites improved with increasing Ni‐MWCNT content. In addition, the effects of various combinations of fillers like silver, copper, and nickel nanoparticles on SE have been studied. Among these nanoparticles, copper nanoparticles in combination with MWCNT and Ni‐MWCNT showed optimal shielding effectiveness of 55 dB. The volume and surface resistivity of the composites decreased with increase in nanofiller content. The tensile strength values were increased by 51% at 0.8 wt% loading of Ni‐MWCNT as compared to that of composite without filler. The improvement in tensile strength was further analyzed using micromechanical models. Cone calorimeter studies showed 25.3% reduction in the peak heat release rate for the composite loaded with 1.5 wt% of Ni‐MWCNT as compared to that of neat PMMA. The nanocomposites also showed enhanced thermal stability with the formation of char as the filler content increased.

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A study of the local convergence of a fifth order iterative method

Cited by 24 publications

References 17 publications

On the Semi-Local Convergence of a Noor–Waseem-like Method for Nonlinear Equations

On the Semi-Local Convergence of a Noor–Waseem-like Method for Nonlinear Equations

Updated and Weaker Convergence Criteria of Newton Iterates for Equations

Polymethyl methacrylate reinforced with nickel coated multi‐walled carbon nanotubes: Flame, electrical and mechanical properties

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