Geodesic
Defining systems and Newton-like methods for finding singular solutions to nonlinear boundary value problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1467-1485 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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M. Yu. Erina; A. F. Izmailov. Defining systems and Newton-like methods for finding singular solutions to nonlinear boundary value problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1467-1485. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a2/

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