SOLUTION TO THE CAUCHY PROBLEM BY NEWTON'S 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:

Cauchy problem, Newton's method, modified Newton-Kantorovich method, Banach space, Fréchet derivative, successive approximations, error estimation

Abstract

This paper examines the application of Newton's method and its modification, the Newton-Kantorovich method, to solving the Cauchy problem. The authors describe the process of transition from algebraic equations to functional equations in Banach spaces and present an algorithm for constructing successive approximations. The article provides a comparative analysis of the effectiveness of Newton's method and the simple iteration method, and also provides a mathematical estimate of the error in the obtained results.

References

1. Канторович Л.В., Акилов Г.П. Функциональный анализ. Наука, М., 1977; 744 с.

2. Лизоркин П.И. Курс дифференциальных и интегральных уравнений. Наука, М., 1981, 384 с.

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Published

2026-06-01

Issue

Vol. 21 No. 1 (2015): СОВРЕМЕННЫЕ ПРОБЛЕМЫ МЕХАНИКИ СПЛОШНЫХ СРЕД

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