Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
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 convergence of the solution of the initial value problem for singularly perturbed higher-order integro-differential equation
Date
2018-01-01
Author
Dauylbayev, M. K.
Akhmet, Marat
Mirzakulova, A. E.
Uaissov, A. B.
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
66
views
0
downloads
Cite This
The article is devoted to research the Cauchy problem for singularly perturbed higher-order linear integro-differential equation with a small parameters at the highest derivatives, provided that the roots of additional characteristic equation have negative signs. An explicit analytical formula of the solution of singularly perturbed Cauchy problem is obtained. The theorem about asymptotic estimate of a solution of the initial value problem is proved. The nonstandard degenerate initial value problem is constructed. We find the solution of the nonstandard degenerate initial value problem. An estimate difference of the solution of a singularly perturbed and nonstandard degenerate initial value problems is obtained. The asymptotic convergence of solution of a singularly perturbed initial value problem to the solution of the nonstandard degenerate initial value problem is established.
Subject Keywords
singular perturbation
,
small parameter
,
the initial functions
,
asymptotics
,
passage to the limit
URI
https://hdl.handle.net/11511/99138
Journal
INTERNATIONAL JOURNAL OF MATHEMATICS AND PHYSICS
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
Nonnormal regression. I. Skew distributions
İslam, Muhammed Qamarul; Yildirim, F (2001-01-01)
In a linear regression model of the type y = thetaX + e, it is often assumed that the random error e is normally distributed. In numerous situations, e.g., when y measures life times or reaction times, e typically has a skew distribution. We consider two important families of skew distributions, (a) Weibull with support IR: (0, infinity) on the real line, and (b) generalised logistic with support IR: (-infinity, infinity). Since the maximum likelihood estimators are intractable in these situations, we deriv...
Asymptotic behavior of linear impulsive integro-differential equations
Akhmet, Marat; YILMAZ, Oğuz (Elsevier BV, 2008-08-01)
Asymptotic equilibria of linear integro-differential equations and asymptotic relations between solutions of linear homogeneous impulsive differential equations and those of linear integro-differential equations are established. A new Gronwall-Bellman type lemma for integro-differential inequalities is proved. An example is given to demonstrate the validity of one of the results.
Asymptotic integration of second-order impulsive differential equations
Akgol, S. D.; Zafer, Ağacık (2018-02-01)
We initiate a study of the asymptotic integration problem for second-order nonlinear impulsive differential equations. It is shown that there exist solutions asymptotic to solutions of an associated linear homogeneous impulsive differential equation as in the case for equations without impulse effects. We introduce a new constructive method that can easily be applied to similar problems. An illustrative example is also given.
Asymptotic behavior of solutions of differential equations with piecewise constant arguments
Akhmet, Marat (Elsevier BV, 2008-09-01)
The main goal of the work is to obtain sufficient conditions for the asymptotic equivalence of a linear system of ordinary differential equations and a quasilinear system of differential equations with piecewise constant argument.
Asymptotic integration of second-order nonlinear delay differential equations
Agarwal, Ravi P.; Ertem, Tuerker; Zafer, Ağacık (2015-10-01)
We study the asymptotic integration problem for second-order nonlinear delay differential equations of the form (p(t)x' (t))' q(t)x(t) = f (t, x(g(t))). It is shown that if a and v are principal and nonprincipal solutions of equation (p(t)x')' q(t)x = 0, then there are solutions x(1)(t) and x(2) (t) of the above nonlinear equation such that x(1)(t) = au(t) o(u(t)), t -> infinity and x(2)(t) = bv(t) o(v(t)), t -> infinity.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. K. Dauylbayev, M. Akhmet, A. E. Mirzakulova, and A. B. Uaissov, “Asymptotic convergence of the solution of the initial value problem for singularly perturbed higher-order integro-differential equation,”
INTERNATIONAL JOURNAL OF MATHEMATICS AND PHYSICS
, vol. 9, no. 1, pp. 50–59, 2018, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/99138.