Электронный каталог

22.1
A30
Akhmet, M. U
    Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби [Текст] / M.U Akhmet // Singularly perturbed linear oscilator with piecewise-constant argument . - Алматы, 2018. - №1(97). - Р. 3-13. - (Journal of Mathematics, Mechanics, Computer Science = Серия математика, механика, информатика)
ББК 22.1

Рубрики: Математика

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кусочно-постоянный аргумент обобщенного типа -- малый параметр -- сингулярное возмущение
Аннотация: The Cauchy problem for singularly perturbed linear differential equation the second order withpiecewise-constant argument is considered in the article. The definition of singularly perturbedlinear harmonic oscillator with piecewise-constant argument is given in the paper. The system offundamental solutions of homogeneous singularly perturbed differential equation with piecewise-constant argument are constructed according to the nonhomogeneous singularly perturbed differ-ential equation with piecewise-constant argument. With the help of the system of fundamentalsolutions, the initial functions are constructed and their asymptotic representation are obtained.By using the reduction method, the analytical formula of the solution of singularly perturbed theinitial value problem with piecewise-constant argument is obtained. In addition, the unperturbedCauchy problem is constructed according to the singularly perturbed Cauchy problem. The so-lution of the unperturbed Cauchy problem is obtained. When the small parameter tends to thezero, the solution of singularly perturbed the Cauchy problem with piecewise-constant argumentapproaches the solution of the unperturbed Cauchy problem with piecewise-constant argument.The theorem on the passage to the limit is proved.
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Доп.точки доступа:
Dauylbaev, M.K
Mirzakulova, A.E
Atakhan, N.