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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 9, Pages 1467–1485 (Mi zvmmf242)  

Defining systems and Newton-like methods for finding singular solutions to nonlinear boundary value problems

M. Yu. Erinaa, A. F. Izmailovb

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119997, Russia
b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: A technique proposed earlier for constructing defining systems, which are a means for finding singular solutions to nonlinear equations, and the Newton-like methods based on this technique are now analyzed from the point of view of their stability with respect to perturbations in the operator of the equation. The results obtained make it possible to extend this approach to nonlinear boundary value problems for ordinary differential equations.

Key words: boundary value problem for ordinary differential equations, singular solution, defining system, regularity, nondegeneracy, Gauss–Newton method, stability.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:9, 1409–1427

Bibliographic databases:

Document Type: Article
UDC: 519.615.5
Received: 28.03.2007

Citation: M. Yu. Erina, A. F. Izmailov, “Defining systems and Newton-like methods for finding singular solutions to nonlinear boundary value problems”, Zh. Vychisl. Mat. Mat. Fiz., 47:9 (2007), 1467–1485; Comput. Math. Math. Phys., 47:9 (2007), 1409–1427

Citation in format AMSBIB
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\by M.~Yu.~Erina, A.~F.~Izmailov
\paper Defining systems and Newton-like methods for finding singular solutions to nonlinear boundary value problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 9
\pages 1467--1485
\mathnet{http://mi.mathnet.ru/zvmmf242}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2387656}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 9
\pages 1409--1427
\crossref{https://doi.org/10.1134/S0965542507090035}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34848819693}


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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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