2017
Том 69
№ 9

Всі номери

Асимптотическое представление решения смешанной задачи для одного класса интегро-дифференциальных уравнений, содержащих малый параметр

Фильчаков П. Ф.

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Абстракт

An approximate method is considered for the conformal mapping of arbitrary simply connected univalent regions which may be means of some elementary function be mapped on a half-plane with an aperture of arbitrary shape cut in it (fig. 1). The mapped function is sought in the form of a section of series (H or (18). Using the method of least squares the problem in the case of series (1) is reduced to the solution of system (13) the coefficients of which are easily calculated by the recurrent formulae (10) and the formulae of numerical quadratures. In the case of series (IS) the problem is reduced to the solution of an analogous system of linear equations (26). Three examples are considered in which the results obtained are compared with exact mapping functions. In § 3 the described method is extended to the case of regions with a finite number of slits.

Зразок цитування: Фильчаков П. Ф. Асимптотическое представление решения смешанной задачи для одного класса интегро-дифференциальных уравнений, содержащих малый параметр // Укр. мат. журн. - 1962. - 14, № 3. - С. 299-307.

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