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

This article is cited in 5 scientific papers (total in 5 papers)

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
Received: 12.02.1996
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
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\paper Transformation of equations with retarded argument to equations with the best argument
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\yr 1998
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\pages 62--68
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\jour Math. Notes
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\vol 63
\issue 1
\pages 55--60
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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet  mathscinet  zmath
    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  crossref  mathscinet  zmath  isi
    3. Kuznetsov, EB, “Parameterization of differential-algebraic equations with retarded argument”, Doklady Mathematics, 75:1 (2007), 87  crossref  mathscinet  zmath  isi  elib  scopus
    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  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath  isi  elib  elib
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