An algorithm for constructing a quasi-regular asymptotic representation for the solution of singularly perturbed linear multi-point boundary value problems with fast and slow variables

Konyaev Yu.A.
Gichev T.R.

Publisher

Федеральное государственное автономное образовательное учреждение высшего образования "Казанский (Приволжский) федеральный университет"

Abstract

The article is devoted to the system epsilondot x=A_{11}(t)x+A_{12}(t)z+f_1(t), dot z=A_{21}(t)x+A_{22}(t)z+f_2(t), where epsilon is a small positive parameter. The points 0=t_1<t_2<dots<t_n=1 are given. A solution x(t,epsilon),z(t,epsilon) of the mentioned system satisfying the multi-point boundary conditions sum^n_{j=1}F_jx(t_j,epsilon)=x^0, z(0,epsilon)=z^0 is to be found. The author gives sufficient conditions when a bounded solution of this problem as epsilonto0 exists. The form of the solution is obtained

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An algorithm for constructing a quasi-regular asymptotic representation for the solution of singularly perturbed linear multi-point boundary value problems with fast and slow variables

Abstract

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An algorithm for constructing a quasi-regular asymptotic representation for the solution of singularly perturbed linear multi-point boundary value problems with fast and slow variables

Abstract

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