ON ONE APPLICATION OF THE NEWTON-KANTOROVICH METHOD

Authors

  • А.М. Osmonkanov Kyrgyz State University of Construction, Transport and Architecture named after N. Isanov image/svg+xml Author
  • E.T. Turgunaliev Kyrgyz State University of Construction, Transport and Architecture named after N. Isanov image/svg+xml Author
  • К.Т. Karybalieva Kyrgyz State University of Construction, Transport and Architecture named after N. Isanov image/svg+xml Author

Keywords:

Newton-Kantorovich method, nonlinear integral equation, iterative process, Fréchet derivative, functional equation, convergence

Abstract

This article examines the application of the generalized Newton–Kantorovich method to solving nonlinear integral equations in Banach spaces. The authors analyze the classical and modified iterative process schemes, emphasizing the computational advantages and convergence rates of each. Using a specific example of a nonlinear equation, the procedure for finding one of two possible solutions is demonstrated, confirming the practical effectiveness of the method in selecting a successful initial approximation.

References

1. Канторович Л.В., Акилов Г.П. Функциональный анализ М.: Наука, 1977 742с.

2. Треногин В.А. Функциональный анализ. М.: Наука, 1980. 496с.

3. Верлань А.Ф., Сизиков В.С. Методы решения интегральных уравнений с программами для ЭВМ. Справочные пособие. Киев: Наукова думка, 1978. 291с.

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Published

2026-06-01

Issue

Vol. 20 No. 2 (2014): СОВРЕМЕННЫЕ ПРОБЛЕМЫ МЕХАНИКИ СПЛОШНЫХ СРЕД

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