Abstract
Connections between solutions to a class of systems of ordinary differential equations of a large dimension and delay equations are studied. A new method is justified for approximation of solutions to delay equations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Likhoshvaĭ V. A., Fadeev S. I., Demidenko G. V., and Matushkin Yu. G., “Modeling multistage synthesis without branching by a delay equation,” Sibirsk. Zh. Industr. Mat., 7, No. 1, 73–94 (2004).
Demidenko G. V. and Likhoshvaĭ V. A., “On differential equations with retarded argument,” Siberian Math. J., 46, No. 3, 417–430 (2005).
Demidenko G. V., Likhoshvaĭ V. A., Kotova T.V., and Khropova Yu. E., “On one class of systems of differential equations and on retarded equations,” Siberian Math. J., 47, No. 1, 45–54 (2006).
Demidenko G. V. and Khropova Yu. E., “On properties of solutions of one delay differential equation,” in: Proceedings of the Fifth International Conference on Bioinformatics of Genome Regulation and Structure (Eds. N. Kolchanov and R. Hofestädt), Novosibirsk, 2006, Vol. 3, pp. 38–42.
Demidenko G. V., “Systems of ordinary differential equations of large dimensions and delay equations,” in: Nonlinear Analysis and Extremal Problems [in Russian], Inst. Syst. Dyn. Cont. Theor. SB RAS, Irkutsk, 2008, pp. 1–34.
Demidenko G. V., Kolchanov N. A., Likhoshvaĭ V. A., Matushkin Yu. G., and Fadeev S. I., “Mathematical simulation of regulatory circuits of gene networks,” Comput. Math. Math. Phys., 44, No. 12, 2166–2183 (2004).
Demidenko G. V., Mel’nik I. A., and Khropova Yu. E., Delay Equations in the Problems of Multistage Substance Synthesis [in Russian] [Preprint, No. 233], Sobolev Inst. Mat. SB RAS, Novosibirsk (2009).
Myshkis A. D., Linear Differential Equations with Retarded Argument [in Russian], Nauka, Moscow (1972).
El’sgol’ts L. E. and Norkin S. B., Introduction to the Theory and Application of Differential Equations with Deviating Arguments, Academic Press, New York and London (1973).
Godunov S. K., Ordinary Differential Equations with Constant Coefficients [in Russian], Novosibirsk Univ., Novosibirsk (1994).
Blatter C., Wavelet Analysis. Theory Fundamentals [Russian translation], Tekhnosfera, Moscow (2004).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text Copyright © 2010 Demidenko G. V. and Mel’nik I. A.
The authors were supported by the Federal Target Program “Scientific and Educational Personnel of Innovative Russia” for 2009–2012 (State Contract 02.740.11.0429), the Russian Foundation for Basic Research (Grant 10-01-00035), and the Interdisciplinary Project of the Siberian Branch of the Russian Academy of Sciences (Grant 107).
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 528–546, May–June, 2010.
Rights and permissions
About this article
Cite this article
Demidenko, G.V., Mel’nik, I.A. On a method of approximation of solutions to delay differential equations. Sib Math J 51, 419–434 (2010). https://doi.org/10.1007/s11202-010-0043-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11202-010-0043-2