J. Nonl. Evol. Equ. Appl. 2011 (1), pp. 1-22, published on July 6, 2011:

Properties of the method of successive approximations for two-point boundary value problems

Alexandru Mihai Bica

Department of Mathematics and Informatics, University of Oradea

Received May 29, 2011
Accepted June 24, 2011

Communicated by Gaston M. N’Guérékata

Abstract.   The convergence and numerical stability properties of the method of successive approximations applied to two-point boundary value problems for nonlinear second order neutral differential equations in Banach spaces are obtained. The constructed algorithm has a practical stopping criterion and its accuracy is illustrated on three numerical examples.
Keywords: Two-point boundary value problem; fixed point technique; approximation of the solution.
2010 Mathematics Subject Classification:   34B15.

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