ASYMPTOTIC EXPANSION OF SOLUTION OF GENERAL BVP WITH INITIAL JUMPS FOR HIGHER-ORDER SINGULARLY PERTURBED INTEGRO-DIFFERENTIAL EQUATION

被引：4

作者：

Dauylbayev, M. K. ^{[1
,4
]}

Atakhan, N. ^{[2
,4
]}

Mirzakulova, A. E. ^{[3
]}

机构：

[1] Al Farabi Kazakh Natl Univ, Alma Ata, Kazakhstan

[2] Kazakh State Womens Teacher Training Univ, Alma Ata, Kazakhstan

[3] Abay Kazakh Natl Pedag Univ, Alma Ata, Kazakhstan

[4] Inst Informat & Computat Technol, Alma Ata, Kazakhstan

来源：

NEWS OF THE NATIONAL ACADEMY OF SCIENCES OF THE REPUBLIC OF KAZAKHSTAN-SERIES PHYSICO-MATHEMATICAL | 2018年 / 6卷 / 322期

关键词：

singular perturbation; the integro-differential equation; a small parameter; asymptotic expansion; the initial jump; the boundary layer;

D O I：

10.32014/2018.2518-1726.14

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：28 / 36

页数：9

共 10 条

[1] A singularly perturbed differential equation with piecewise constant argument of generalized type
Akhmet, Marat
Dauylbayev, Muratkhan
Mirzakulova, Aziza
[J]. TURKISH JOURNAL OF MATHEMATICS, 2018, 42 (04) : 1680 - 1685
[2] Atakhan N., 2016, 3 INT C AN APPL MATH, P45
[3] Atakhan N., 2017, 5 AB DHAB U ANN INT, P28
[4] Dauylbaev MK, 2017, J MATH SCI, V222, P214, DOI [10.1007/s10958-017-3294-7, DOI 10.1007/S10958-017-3294-7]
[5] Dauylbaev MK, 2016, J DISCONTINUITY NONL, V5, P147
[6] THE INITIAL JUMPS OF SOLUTIONS AND INTEGRAL TERMS IN SINGULAR BVP OF LINEAR HIGHER ORDER INTEGRO-DIFFERENTIAL EQUATIONS
Dauylbayev, M. K.
Atakhan, N.
[J]. MISKOLC MATHEMATICAL NOTES, 2015, 16 (02) : 747 - 761
[7] Dauylbayev M. K., 2017, NEWS NATL ACAD SC PM, V312, P18
[8] Kasymov K.A., 2003, UKR MATH J+, V55, P1777
[9] Asymptotic estimates of the solution of a singularly perturbed boundary value problem with an initial jump for linear differential equations
Kasymov, KA
Nurgabyl, DN
[J]. DIFFERENTIAL EQUATIONS, 2004, 40 (05) : 641 - 651
[10] Construction of the solution of the boundary value problem for integro differential equation with a small parameter in highest derivatives
Mirzakulova, A. E.
Atakhan, N.
[J]. BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2016, 84 (04): : 99 - 103

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