Open Access

Generalized quasilinearization method and higher order of convergence for second-order boundary value problems

Boundary Value Problems20062006:25715

https://doi.org/10.1155/BVP/2006/25715

Received: 24 March 2005

Accepted: 19 September 2005

Published: 18 March 2006

Abstract

The method of generalized quasilinearization for second-order boundary value problems has been extended when the forcing function is the sum of -hyperconvex and -hyperconcave functions. We develop two sequences under suitable conditions which converge to the unique solution of the boundary value problem. Furthermore, the convergence is of order . Finally, we provide numerical examples to show the application of the generalized quasilinearization method developed here for second-order boundary value problems.

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Authors’ Affiliations

(1)
Department of Mathematics, University of Louisiana at Lafayette

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Copyright

© Melton and Vatsala 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.