https://elib.bsu.by:443/handle/123456789/185744 2026-04-20T08:04:45Z https://elib.bsu.by:443/handle/123456789/344806 Заглавие документа: Volterra type integral equations with conjugation / A. P. Shilin // Differential Equations Авторы: Shilin, A.P. Аннотация: h e solution of Volterra integral equations with kernels depending on the difference of the arguments on the half-line is a well-known example in which operational calculus is used effectively. It is less known that such equations can also be solved on a finite interval. The corresponding formulas call be found in [1]: they are based on the Fourier integral transform. 2000-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/344805 Заглавие документа: Интегральные уравнения типа уравнений Вольтерра с сопряжением Авторы: Шилин, А.П. Аннотация: Решены два линейных интегральных уравнения второго рода на конечном интервале. Левые части уравнений помимо интегралов, характерных для уравнений Вольтерра, содержат еще интегралы специального вида с комплексно-сопряженным значением неизвестной функции. 2000-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/344804 Заглавие документа: The convergence rate of economical iterative methods for stationary problems of mathematical physics Авторы: Abrashin, V.N.; Zhadaeva, N.G. Аннотация: Nonstationary equations or related finite-difference schemes are used for solving stationary problems of mathematical physics. By [1, p. 550; 2, p. 320], a solution of a stationary problem with positive operators can be treated as a limit (as t ~ oc) solution of the corresponding nonstationary problem. There is extensive literature dealing with this problem [1-9]. Economical iterative methods are especially interesting. They include the classical alternating direction method [1-3], various decomposition methods [7, 8], and factorized methods [1, 2], for which the convergence rate have been analyzed in detail and the possibility of increasing the convergence rate by an appropriate choice of the iteration parameters has been indicated [1, 2, 4, 6-10]. Efficient parallel algorithms have been suggested for economical iterative methods. However, the above-mentioned classical methods have a number of disadvantages; namely, the number of decomposition components is restricted, these components must commute, and the convergence rate is not very high. A many-component alternating direction method free of these disadvantages was suggested in [11-13]. The papers [14, 15] deal with the investigation of iterative methods for stationary problems on the basis of lnany-component finite-difference schemes. In the present paper, we analyze the convergence rate of these methods and issues related to the optimal choice of the iteration parameter. 2000-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/344802 Заглавие документа: О скорости сходимости экономичных итерационных методов для стационарных задач математической физики Авторы: Абрашин, В.Н.; Абрашина-Жадаева, Н.Г. Аннотация: Изучаются многокомпонентные аддитивные итерационные методы решения многомерных задач математической физики. Рассматриваются двух- и трехслойные итерационные методы, исследуется их скорость сходимости в различных нормах. 2000-01-01T00:00:00Z