Analysis of systems of singular ordinary differential equations
type: Item
instance of: scholarly article
title: Analysis of systems of singular ordinary differential equations
zbMATH Open document ID: 0962.65055
DOI: 10.1007/BF02733411
author: V. V. Grigorenko
author: I. M. Romanishin
author: L. A. Sinitskii
published in: Cybernetics and Systems Analysis
publication date: 2000-09-13T00:00:00Z
review text: Systems of ordinary differential equations with a small parameter at the derivative and specific features of the construction of their periodic solutions are considered. Sufficient conditions for the existence and uniqueness of such a periodic solution is presented. An iterative procedure of the construction of the steady-state of a system of differential equations with a small parameter at the derivative is proposed. This iterative procedure is reduced to the solution of a system of nonlinear algebraic equations and does not involve the integration of the system of differential equations. The problem of numerical approximation of the solution is considered based on the proposed procedure. Some sources of possible divergence of this procedure are found and sufficient conditions for the convergence of the proposed procedure are proved. The results of some numerical experiments are presented and compared with the results of the theory.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 1505749
zbMATH Keywords: systems of singular ordinary differential equations
zbMATH Keywords: iterative method
zbMATH Keywords: singular perturbations
zbMATH Keywords: small parameter
zbMATH Keywords: periodic solution
zbMATH Keywords: system of nonlinear algebraic equations
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiments
reviewed by: Jiří Vaníček
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1505749