Analysis of systems of singular ordinary differential equations |
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Authors: | V V Grigorenko I M Romanishin L A Sinitskii |
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Affiliation: | (1) I. Franko State University, Lvov, Ukraine;(2) Physicomechanical Institute of the National Academy of Sciences of Ukraine, Lvov, Ukraine |
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Abstract: | Systems of ordinary differential equations with a small parameter at the derivative and specific features of the construction
of their periodic solution are considered. Sufficient conditions of existence and uniqueness of the periodic solution are
presented. An iterative procedure of construction of the steady-state solution of a system of differential equations with
a small parameter at the derivative is proposed. This 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. Problems of numerical calculation
of the solution are considered based on the procedure proposed. Some sources of its divergence are found, and the sufficient
conditions of its convergence are obtained. The results of numerical experiments are presented and compared with theoretical
ones.
Translated from Kibemetika i Sistemnyi Analiz, No. 5, pp. 103–110, September–October, 1999. |
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Keywords: | system of ordinary differential equations small parameter periodic solution numerical calculation iterative procedure |
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