Asymptotic convergence of the solution for singularly perturbed boundary value problem with boundary jumps

被引：3
|
作者：
Mirzakulova, A. E. [1 ]
Atakhan, N. [2 ]
Asset, N. [3 ]
Rysbek, A. [1 ]
机构：
[1] Abay Kazakh Natl Pedag Univ, Alma Ata, Kazakhstan
[2] Kazakh State Womens Teacher Training Univ, Alma Ata, Kazakhstan
[3] Nazarbayev Intellectual Sch, Alma Ata, Kazakhstan
来源：
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS | 2018年 / 92卷 / 04期
关键词：
singular perturbation; small parameter; the boundary jump; the initial jump; boundary functions; asymptotic;
D O I：
10.31489/2018M4/64-71
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The 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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页码：64 / 71
页数：8
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