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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 6, Pages 934–957 (Mi zvmmf10545)  

This article is cited in 4 scientific papers (total in 4 papers)

Parametrization of the Cauchy problem for systems of ordinary differential equations with limiting singular points

E. B. Kuznetsov, S. S. Leonov

Moscow State Aviation Institute, Moscow, Russia

Abstract: The method of solution continuation with respect to a parameter is used to solve an initial value problem for a system of ordinary differential equations with several limiting singular points. The solution is continued using an argument (called the best) measured along the integral curve of the problem. Additionally, a modified argument is introduced that is locally equivalent to the best one in the considered domain. Theoretical results are obtained concerning the conditioning of the Cauchy problem parametrized by the modified argument in a neighborhood of each point of its integral curve.

Key words: method of solution continuation with respect to a parameter, best parametrization, limiting singular point, system of ordinary differential equations, initial value problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-08-00943_а


DOI: https://doi.org/10.7868/S0044466917060102

Full text: PDF file (361 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:6, 931–952

Bibliographic databases:

UDC: 519.62
Received: 18.05.2016
Revised: 14.07.2016

Citation: E. B. Kuznetsov, S. S. Leonov, “Parametrization of the Cauchy problem for systems of ordinary differential equations with limiting singular points”, Zh. Vychisl. Mat. Mat. Fiz., 57:6 (2017), 934–957; Comput. Math. Math. Phys., 57:6 (2017), 931–952

Citation in format AMSBIB
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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. Karpov V.V., Ignat'ev O.V., Semenov A.A., “The Stress-Strain State of Ribbed Shell Structures”, Mag. Civ. Eng., 74:6 (2017), 147–160  crossref  isi
    2. E. B. Kuznetsov, S. S. Leonov, “Examples of parametrization of the Cauchy problem for systems of ordinary differential equations with limiting singular points”, Comput. Math. Math. Phys., 58:6 (2018), 881–897  mathnet  crossref  crossref  isi  elib
    3. A. A. Semenov, S. S. Leonov, “Metod nepreryvnogo prodolzheniya resheniya po nailuchshemu parametru pri raschete obolochechnykh konstruktsii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 161, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2019, 230–249  mathnet  crossref  elib
    4. K. G. Kozhobekov, D. A. Tursunov, “Asimptotika resheniya kraevoi zadachi, kogda predelnoe uravnenie imeet neregulyarnuyu osobuyu tochku”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:3 (2019), 332–340  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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