Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
ASYMPTOTIC EXPANSION OF THE SOLUTION FOR SINGULAR PERTURBED LINEAR IMPULSIVE SYSTEMS
Download
document.pdf
Date
2024-06-30
Author
Dauylbayev, M.K.
Akhmet, Marat
Aviltay, N.
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
39
views
8
downloads
Cite This
In this study, a singularly perturbed linear impulsive system with singularly perturbed impulses is considered. Many books discuss different types of singular perturbation problems. In the present work, an impulse system is considered in which a small parameter is introduced into the impulse equation. This is the main novelty of our study, since other works [25] have only considered a small parameter in the differential equation. A necessary condition is also established to prevent the impulse function from bloating as the parameter approaches zero. As a result, the notion of singularity for discontinuous dynamics is greatly extended. An asymptotic expansion of the solution of a singularly perturbed initial problem with an arbitrary degree of accuracy for a small parameter is constructed. A theorem for estimating the residual term of the asymptotic expansion is formulated, which estimates the difference between the exact solution and its approximation. The results extend those of [32], which formulates an analogue of Tikhonov’s limit transition theorem. The theoretical results are confirmed by a modelling example.
Subject Keywords
differential equations with singular impulses
,
singular perturbation
,
small parameter
URI
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85203811537&origin=inward
https://hdl.handle.net/11511/111093
Journal
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
DOI
https://doi.org/10.26577/jmmcs2024-122-02-b2
Collections
Department of Mathematics, Article
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. K. Dauylbayev, M. Akhmet, and N. Aviltay, “ASYMPTOTIC EXPANSION OF THE SOLUTION FOR SINGULAR PERTURBED LINEAR IMPULSIVE SYSTEMS,”
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
, vol. 122, no. 2, pp. 14–26, 2024, Accessed: 00, 2024. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85203811537&origin=inward.