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Dergiler / Results in Nonlinear Analysis / 2026 / 2022 - Cilt 5, Sayı 4

BROADENING THE CONVERGENCE DOMAIN OF SEVENTH-ORDER METHOD SATISFYING LIPSCHITZ AND HOLDER CONDITIONS

J. P. Jaiswal(Guru Ghasidas Vishwavidyalaya)
Akanksha Saxena(Maulana Azad National Institute of Technology)
Kamal Raj Paradasani(Maulana Azad national Institute of Technology)
Sayfa
473–486
Yayın Tarihi
2022-12-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

At last, we estimated the radii of the convergence balls using a variety of numerical examples, including a nonlinear Hammerstein equation.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The local convergence analysis of a seventh order algorithm for solving nonlinear equations is presented in the current discussion by assuming that the ?rst-order Fréchet derivative belongs to the Lipschitz class.
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Temel Bulgular & Veri:This approach yields radii of convergence ball, error bound and uniqueness of the solution.
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Sonuç & Katkı:At last, we estimated the radii of the convergence balls using a variety of numerical examples, including a nonlinear Hammerstein equation.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Nonlinear equation · Banach space · local convergence

Abstract

The local convergence analysis of a seventh order algorithm for solving nonlinear equations is presented in the current discussion by assuming that the ?rst-order Fréchet derivative belongs to the Lipschitz class. This approach yields radii of convergence ball, error bound and uniqueness of the solution. Further, generalization of the study extended by considering Hölder continuity condition. At last, we estimated the radii of the convergence balls using a variety of numerical examples, including a nonlinear Hammerstein equation.

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Bu Makaleye Atıf Yap

Jaiswal, J. P., Saxena, A., Paradasani, K. R. (2022). BROADENING THE CONVERGENCE DOMAIN OF SEVENTH-ORDER METHOD SATISFYING LIPSCHITZ AND HOLDER CONDITIONS. Results in Nonlinear Analysis, 2022 - Cilt 5, Sayı 4, 473–486. https://doi.org/10.53006/rna.1146027

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