Singularly perturbed linear oscillator with piecewise-constant argument

Akhmet, Marat; Dauylbayev, M. K.; Mirzakulova, A.E.; Atakhan, N.

doi:10.26577/jmmcs-2018-1-480

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Researchers [1][2][3][4][5][6][7][8][9][10][11][12][13][14] have developed efficient asymptotic methods for singularly perturbed problems. For sufficiently small values of the parameter, these methods make it possible to construct uniform asymptotic approximations.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic estimations of the solution for a singularly perturbed equation with unlimited boundary conditions

Atakhan¹,

Nurpeisov²,

Konisbayeva³

2022

Bul. Kar. Univ. - Math.

View full text Add to dashboard Cite

The paper studies a two-point boundary value problem with unlimited boundary conditions for a linear singularly perturbed differential equation. Asymptotic estimates are given for a linearly independent system of solutions of a homogeneous perturbed equation. Auxiliary, so-called boundary functions, the Cauchy function are defined. For sufficiently small values of the parameter, estimates for the Cauchy function and boundary functions are found. An algorithm for constructing the desired solution of the boundary value problem has been developed. A theorem on the solvability of a solution to a boundary value problem is proved. For sufficiently small values of the parameter, an asymptotic estimate for the solution of the inhomogeneous boundary value problem is established. The initial conditions for the degenerate equation are determined. The formula is determined; the phenomena of the initial jump are studied.

show abstract