Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет

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Автор: search.filters.author.A. E. Mirzakulova

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    Singularly perturbed linear oscillator with piecewise-constant argument
    (Al-Farabi Kazakh National University, 2018-08-27)
    Marat U. Akhmet
    ;
    M. K. Dauylbayev
    ;
    A. E. Mirzakulova
    ;
    Н. Атахан
    The Cauchy problem for singularly perturbed linear differential equation the second order with piecewise-constant argument is considered in the article. The definition of singularly perturbed linear harmonic oscillator with piecewise-constant argument is given in the paper. The system of fundamental solutions of homogeneous singularly perturbed differential equation with piecewiseconstant argument are constructed according to the nonhomogeneous singularly perturbed differential equation with piecewise-constant argument. With the help of the system of fundamental solutions, 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 the initial value problem with piecewise-constant argument is obtained. In addition, the unperturbed Cauchy problem is constructed according to the singularly perturbed Cauchy problem. The solution of the unperturbed Cauchy problem is obtained. When the small parameter tends to the zero, the solution of singularly perturbed the Cauchy problem with piecewise-constant argument approaches 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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    ASYMPTOTIC EXPANSION OF SOLUTION OF GENERAL BVP WITH INITIAL JUMPS FOR HIGHER-ORDER SINGULARLY PERTURBED INTEGRO-DIFFERENTIAL EQUATION
    (2018-12-15)
    M. K. Dauylbayev
    ;
    Н. Атахан
    ;
    A. E. Mirzakulova
    In this article we constructed an asymptotic expansion of the solution undivided boundary value problem for singularly perturbed integro-differential equations with an initial jump phenomenon m – th order. We obtain the theorem about estimation of the remainder term’s asymptotic with any degree of accuracy in the smallparameter.
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    Asymptotic convergence of the solution for singularly perturbed boundary value problem with boundary jumps
    (Karaganda Buketov University, 2018-12-30)
    A. E. Mirzakulova
    ;
    Н. Атахан
    ;
    N. Asset
    ;
    А.С. Рысбек
    Asymptotic convergence of the solution for singularly perturbed boundary value problem with boundary jumpsThe article is devoted to study of boundary value problem with boundary jumps for third order linear integro-differential equation with a small parameter at the highest derivatives, provided that additional characteristic equation's roots have opposite signs.The modified unperturbed boundary value problem is constructed.The solution of modified unperturbed problem is obtained.Initial jumps' values of the integral term and solution are defined.An estimate difference of solution for singularly perturbed and modified unperturbed boundary value problems is obtained.The convergence of solution for singularly perturbed boundary value problem to solution of modified unperturbed boundary value problem is proved.
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