Boundary Value Problems
Volume 2006 (2006), Article ID 25715, 15 pages
Generalized quasilinearization method and higher order of convergence for second-order boundary value problems
Department of Mathematics, University of Louisiana at Lafayette, Lafayette 70504-1010, LA, USA
Received 24 March 2005; Revised 13 September 2005; Accepted 19 September 2005
Copyright © 2006 Tanya G. Melton and A. S. Vatsala. 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.
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.