Asymptotic Convergence of the Solution of a Singularly Perturbed Integro-Differential Boundary Value Problem
- Authors
- Zhumanazarova, Assiya; Cho, Young Im
- Issue Date
- Feb-2020
- Publisher
- MDPI
- Keywords
- small parameter; singular perturbation; boundary functions; asymptotic estimates
- Citation
- MATHEMATICS, v.8, no.2
- Journal Title
- MATHEMATICS
- Volume
- 8
- Number
- 2
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/26147
- DOI
- 10.3390/math8020213
- ISSN
- 2227-7390
- Abstract
- In this study, the asymptotic behavior of the solutions to a boundary value problem for a third-order linear integro-differential equation with a small parameter at the two higher derivatives has been examined, under the condition that the roots of the additional characteristic equation are negative. Via the scheme of methods and algorithms pertaining to the qualitative study of singularly perturbed problems with initial jumps, a fundamental system of solutions, the Cauchy function, and the boundary functions of a homogeneous singularly perturbed differential equation are constructed. Analytical formulae for the solutions and asymptotic estimates of the singularly perturbed problem are obtained. Furthermore, a modified degenerate boundary value problem has been constructed, and it was stated that the solution of the original singularly perturbed boundary value problem tends to this modified problem's solution.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - IT융합대학 > 컴퓨터공학과 > 1. Journal Articles
![qrcode](https://api.qrserver.com/v1/create-qr-code/?size=55x55&data=https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/26147)
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.