Asymptotic Convergence of the Solution of a Singularly Perturbed Integro-Differential Boundary Value Problem

Assiya Zhumanazarova and Young Im Cho
Additional contact information
Assiya Zhumanazarova: Department of Computer Engineering, Gachon University, Gyeonggi-do 461-701, Korea
Young Im Cho: Department of Computer Engineering, Gachon University, Gyeonggi-do 461-701, Korea

Mathematics, 2020, vol. 8, issue 2, 1-17

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.

Keywords: small parameter; singular perturbation; boundary functions; asymptotic estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/2/213/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/2/213/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:2:p:213-:d:317865

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().