№ 58-2. Том 2: ОБРАЗОВАНИЕ И НАУКА В XXI ВЕКЕ, Январь, 2025
Научно-образовательные статьи

REGULAR METHODS FOR APPROXIMATE SOLUTIONS OF FIRST-TYPE INTEGRAL EQUATIONS

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  • Nuriddinova (Pulatova) Mushtariy Shuhratjon qizi
Nuriddinova (Pulatova) Mushtariy Shuhratjon qizi
Namangan State University, Master’s student

Опубликован 21.01.2025

Ключевые слова

  • Volterra and Fredholm Integral Equations,
  • Tikhonov Regularization,
  • Iterative Methods,
  • Hybrid Techniques

Как цитировать

M. Sh. Nuriddinova (Pulatova). (2025). REGULAR METHODS FOR APPROXIMATE SOLUTIONS OF FIRST-TYPE INTEGRAL EQUATIONS. ОБРАЗОВАНИЕ И НАУКА В XXI ВЕКЕ, 58-2. Том 2. https://mpcareer-google.ru/index.php/journal/article/view/691

Аннотация

This article provides a comprehensive study of solving first-type integral equations using regular methods. It highlights the theoretical foundations of Volterra and Fredholm integral equations, discussing the challenges posed by their ill-posedness. The focus is on approximation techniques such as Tikhonov regularization, iterative methods, and hybrid strategies. Applications in real-world scenarios are presented, alongside numerical examples to validate the effectiveness of these methods.

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Библиографические ссылки

  1. Tikhonov, A. N., and Arsenin, V. Y., 'Solutions of Ill-Posed Problems,' Winston & Sons, 1977.
  2. Kress, R., 'Linear Integral Equations,' Springer, 1999.
  3. Groetsch, C. W., 'The Theory of Tikhonov Regularization for Fredholm Equations,' Springer, 1984.
  4. Hansen, P. C., 'Rank-Deficient and Discrete Ill-Posed Problems,' SIAM, 1998.