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

M. Yu. Erina^a, A. F. Izmailov<sup>b

a</sup> 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.

UDC: 519.615.5

Received: 28.03.2007

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

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