On the Construction of Asymptotics of the Solution of Multipoint Boundary-Value Problem for a Linear Degenerate Singularly Perturbed System of Differential Equations

2016 ◽  
Vol 217 (4) ◽  
pp. 385-398
Author(s):  
M. B. Vira
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
System Of Differential Equations ◽  
Singularly Perturbed System ◽  
Multipoint Boundary ◽  
Perturbed System ◽  
Linear Degenerate ◽  
Multipoint Boundary Value Problem

Existence, uniqueness and asymptotic expansion of the solution of a multipoint boundary-value problem with parameters for a singularly-perturbed system of integro-differential equations

1982 ◽  
Vol 92 (1-2) ◽  
pp. 103-112 ◽  
Author(s):  
S. G. Hristova ◽  
D. D. Bainov
Keyword(s):  
Boundary Condition ◽  
Asymptotic Expansion ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Singularly Perturbed ◽  
Linear Boundary ◽  
Singularly Perturbed System ◽  
Linear Boundary Condition ◽  
Perturbed System ◽  
Multipoint Boundary Value Problem

SynopsisAn asymptotic expansion in powers of the small parameter of the solution of a singularly-perturbed system of integro-differential equations with a non-linear boundary condition set at several points of the interval considered is constructed and verified.

ASYMPTOTIC SOLUTIONS OF A TWO-POINT EDGE-BASED PROBLEM FOR A LINEAR SINGULARLY DISTURBED SYSTEM OF DIFFERENTIAL EQUATIONS IN NONCRITICAL AND CRITICAL STABLE CASES

2019 ◽  
pp. 19-25
Author(s):  
S. Pafyk
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Asymptotic Solution ◽  
Asymptotic Methods ◽  
Singularly Perturbed ◽  
Asymptotic Estimates ◽  
System Of Differential Equations ◽  
Singularly Perturbed System ◽  
Perturbed System ◽  
Edge Based

Using asymptotic methods in the theory of differential equations and their systems, an asymptotic solution of the boundary value problem for a linear singularly perturbed system of differential equations is constructed. Considered non-critical and critical resistant cases. For each of the cases, the corresponding asymptotic estimates were found.

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