Boundary Value Problems 
Volume 2006 (2006), Article ID 25715, 15 pages
doi:10.1155/BVP/2006/25715

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

Tanya G. Melton and A. S. Vatsala

 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

Abstract

The method of generalized quasilinearization for second-order boundary value problems has been extended when the forcing function is the sum of 2-hyperconvex and 2-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 3. Finally, we provide numerical examples to show the application of the generalized quasilinearization method developed here for second-order boundary value problems.