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22.1
M75
Mirzakulova, A. E
The Cauchy problem for sinqularly perturbed hiqher-order inteqro-differential equations [Текст] / A.E Mirzakulova // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КАЗНУ им Аль - Фараби. - Алматы, 2018. - №1(97). - Р. 14-24. - (Математика, механика, информатика сериясы = Серия математика, механика, информатика)
ББК 22.1
Рубрики: Математика
Кл.слова (ненормированные):
сингулярное возмущение -- малый параметр -- начальные функции -- асимптотика -- предельный переход
Аннотация: The article is devoted to research the Cauchy problem for singularly perturbed higher-order linearintegro-differential equation with a small parameter at the highest derivatives, provided that theroots of additional characteristic equation have negative signs. The aim of this paper is to bringasymptotic estimation of the solution of a singularly perturbed Cauchy problem and the asymptoticconvergence of the solution of a singularly perturbed initial value problem to the solution ofan unperturbed initial value problem. In this paper the fundamental system of solutions, initialfunctions of a singularly perturbed homogeneous differential equation are constructed and theirasymptotic estimates are obtained. By using the initial functions, we obtain an explicit analyticalformula of the solution. The theorem about asymptotic estimate of a solution of the initial valueproblem is proved. The unperturbed Cauchy problem is constructed. We find the solution of theunperturbed Cauchy problem. An estimate difference of the solution of a singularly perturbedand unperturbed initial value problems. The asymptotic convergence of solution of a singularlyperturbed initial value problem to the solution of the unperturbed initial value problem is proved.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Dauylbaev, M.K
Akhmet, M.U
Dzhetpisbaeva, A.K
M75
Mirzakulova, A. E
The Cauchy problem for sinqularly perturbed hiqher-order inteqro-differential equations [Текст] / A.E Mirzakulova // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КАЗНУ им Аль - Фараби. - Алматы, 2018. - №1(97). - Р. 14-24. - (Математика, механика, информатика сериясы = Серия математика, механика, информатика)
Рубрики: Математика
Кл.слова (ненормированные):
сингулярное возмущение -- малый параметр -- начальные функции -- асимптотика -- предельный переход
Аннотация: The article is devoted to research the Cauchy problem for singularly perturbed higher-order linearintegro-differential equation with a small parameter at the highest derivatives, provided that theroots of additional characteristic equation have negative signs. The aim of this paper is to bringasymptotic estimation of the solution of a singularly perturbed Cauchy problem and the asymptoticconvergence of the solution of a singularly perturbed initial value problem to the solution ofan unperturbed initial value problem. In this paper the fundamental system of solutions, initialfunctions of a singularly perturbed homogeneous differential equation are constructed and theirasymptotic estimates are obtained. By using the initial functions, we obtain an explicit analyticalformula of the solution. The theorem about asymptotic estimate of a solution of the initial valueproblem is proved. The unperturbed Cauchy problem is constructed. We find the solution of theunperturbed Cauchy problem. An estimate difference of the solution of a singularly perturbedand unperturbed initial value problems. The asymptotic convergence of solution of a singularlyperturbed initial value problem to the solution of the unperturbed initial value problem is proved.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Dauylbaev, M.K
Akhmet, M.U
Dzhetpisbaeva, A.K
Страница 1, Результатов: 1