Asymptotics of the General Solution of Linear Singularly Perturbed Systems of Higher-Order Differential Equations with Degeneration in the Case of Multiple Spectrum of the Limiting Matrix Pencil

2015 ◽  
Vol 212 (3) ◽  
pp. 305-325 ◽  
Author(s):  
S. P. Pafyk ◽  
V. P. Yakovets’
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Matrix Pencil ◽  
Higher Order ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Perturbed Systems ◽  
Higher Order Differential Equations

scholarly journals Nonlinear singularly perturbed systems of differential equations: A survey

1995 ◽  
Vol 1 (4) ◽  
pp. 275-301
Author(s):  
Angela Slavova
Keyword(s):  
Differential Equations ◽  
Singular Perturbations ◽  
Point Of View ◽  
Singularly Perturbed ◽  
Theory Theory ◽  
Singularly Perturbed Systems ◽  
Constructive Methods ◽  
Systems Of Differential Equations ◽  
Perturbed Systems

In this paper a survey of the most effective methods in singular perturbations is presented. Many applied problems can be modeled by nonlinear singularly perturbed systems, as, for example, problems in kinetics, biochemistry, semiconductors theory, theory of electrical chains, economics, and so on. In this survey we consider averaging and constructive methods that are very useful from the point of view of their numerical and computer realizations.

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