Approximate Solving of the Third Boundary Value Problems for Helmholtz Equations in the Plane with Parallel Cuts

Автор(и)

  • V.D. Dushkin

DOI:

https://doi.org/10.15407/mag13.03.254

Ключові слова:

приближенное решение краевых интегральных уравнений, сингулярное интегральное уравнение, существование приближенного решения, скорость сходимости приближенного решения.

Анотація

В работе предложен метод приближенного решения краевых интегральных уравнений исходной задачи. Системы краевых интегральных уравнений этой задачи получены методом параметрического представления интегральных преобразований. Сходимость приближенных решений к точному решению исходной задачи гарантирована утверждениями, доказанными в этой работе. Найдена также скорость сходимости приближенных решений к точному решению.

Анотацiя

У роботi запропоновано метод наближеного розв'язання крайових iнтегральних рiвнянь вихiдної задачi. Систему крайових iнтегральних рiвнянь цiєї задачi одержано методом параметричного зображення iнтегральних перетворень. Збiжнiсть наближених розв'язкiв до точного розв'язку вихiдної проблеми гарантовано твердженнями, доведеними в цiй роботi. Знайдено також швидкiсть збiжностi наближених розв'язкiв до точного розв'язку.

Mathematics Subject Classification: 45P05, 45L05.

Посилання

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Опубліковано

2017-12-17

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Dushkin, V. Approximate Solving of the Third Boundary Value Problems for Helmholtz Equations in the Plane With Parallel Cuts. J. Math. Phys. Anal. Geom. 2017, 13, 254-267.

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