Asymptotics of the Solution of the Cauchy Problem with an Unstable Spectrum and Prolonging Loss of Stability

The article is devoted to construct a complete asymptotic expansion of the solution to the Cauchy problem for a linear analytical system of singularly perturbed ordinary differential equations of the first order. The peculiarities of the Cauchy problem are that a small parameter is present in front...

Full description

Saved in:
Bibliographic Details
Published in:Lobachevskii journal of mathematics 2024-03, Vol.45 (3), p.1309-1317
Main Authors: Tursunov, D. A., Sadieva, A. S., Kozhobekov, K. G., Tursunov, E. A.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Asymptotic methods
Asymptotic series
Cauchy problems
Differential equations
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Parameter modification
Probability Theory and Stochastic Processes
Stability
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The article is devoted to construct a complete asymptotic expansion of the solution to the Cauchy problem for a linear analytical system of singularly perturbed ordinary differential equations of the first order. The peculiarities of the Cauchy problem are that a small parameter is present in front of the derivative, and the stability conditions are violated in the region under consideration. By modifying the method of boundary functions, a formal asymptotic expansion of the solution to the Cauchy problem is constructed. The remainder term of the expansion is estimated by the idea of L.S. Pontryagin entering the complex plane.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224600845