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 Mat. Zametki, 1998, Volume 63, Issue 1, Pages 62–68 (Mi mz1248)

Transformation of equations with retarded argument to equations with the best argument

E. B. Kuznetsov

Moscow Aviation Institute

Abstract: The problem of choosing the best argument in the Cauchy problem for a system of ordinary differential equations with retarded argument is studied from the viewpoint of the method of continuation of the solution with respect to a parameter. It is proved that the arc length counted along the integral curve of the problem is the best argument for the system of continuation equations to be well-posed in the best possible way. A transformation of the Cauchy problem to the best argument is obtained.

DOI: https://doi.org/10.4213/mzm1248

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English version:
Mathematical Notes, 1998, 63:1, 55–60

Bibliographic databases:

UDC: 517.91+519.622
Revised: 06.06.1997

Citation: E. B. Kuznetsov, “Transformation of equations with retarded argument to equations with the best argument”, Mat. Zametki, 63:1 (1998), 62–68; Math. Notes, 63:1 (1998), 55–60

Citation in format AMSBIB
\Bibitem{Kuz98} \by E.~B.~Kuznetsov \paper Transformation of equations with retarded argument to equations with the best argument \jour Mat. Zametki \yr 1998 \vol 63 \issue 1 \pages 62--68 \mathnet{http://mi.mathnet.ru/mz1248} \crossref{https://doi.org/10.4213/mzm1248} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1631840} \zmath{https://zbmath.org/?q=an:0919.34061} \transl \jour Math. Notes \yr 1998 \vol 63 \issue 1 \pages 55--60 \crossref{https://doi.org/10.1007/BF02316143} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000075520700007} 

• http://mi.mathnet.ru/eng/mz1248
• https://doi.org/10.4213/mzm1248
• http://mi.mathnet.ru/eng/mz/v63/i1/p62

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This publication is cited in the following articles:
1. A. V. Kopylov, E. B. Kuznetsov, “An approach to the numerical integration of the Cauchy problem for delay differential equations”, Comput. Math. Math. Phys., 41:10 (2001), 1470–1479
2. Kopylov, A, “The best parameterization of initial value problem for mixed difference-differential equation”, Computational Science - Iccs 2003, Pt II, Proceedings, 2658 (2003), 507
3. Kuznetsov, EB, “Parameterization of differential-algebraic equations with retarded argument”, Doklady Mathematics, 75:1 (2007), 87
4. E. B. Kuznetsov, V. N. Mikryukov, “Numerical integration of systems of delay differential-algebraic equations”, Comput. Math. Math. Phys., 47:1 (2007), 80–92
5. S. S. Dmitriev, E. B. Kuznetsov, “Numerical solution to systems of delay integrodifferential algebraic equations”, Comput. Math. Math. Phys., 48:3 (2008), 406–419
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