Geodesic
A parametrization method for solving nonlinear two-point boundary value problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 39-63

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A sharper version of the local Hadamard theorem on the solvability of nonlinear equations is proved. Additional parameters are introduced, and a two-parameter family of algorithms for solving nonlinear two-point boundary value problems is proposed. Conditions for the convergence of these algorithms are given in terms of the initial data. Using the right-hand side of the system of differential equations and the boundary conditions, equations are constructed from which initial approximations to the unknown parameters can be found. A criterion is established for the existence of an isolated solution to a nonlinear two-point boundary value problem. This solution is shown to be a continuous function of the data specifying the problem. 
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     title = {A~parametrization method for solving nonlinear two-point boundary value problems},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a5/}
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D. S. Dzhumabaev; S. M. Temesheva. A parametrization method for solving nonlinear two-point boundary value problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 39-63. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a5/