Electron. J. Diff. Eqns., Vol. 2002(2002), No. 90, pp. 1-12.

Generalized quasilinearization method for a second order three point boundary-value problem with nonlinear boundary conditions

Bashir Ahmad, Rahmat Ali Khan, & Paul W. Eloe

Abstract:
The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order differential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order k.

Submitted March 14, 2002. Published October 22, 2002.
Math Subject Classifications: 34B10, 34B15.
Key Words: Generalized quasilinearization, boundary value problem, nonlinear boundary conditions, quadratic and rapid convergence.

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Bashir Ahmad
Department of Mathematics, King Abdulaziz University
Jeddah-21589, Saudi Arabia
e-mail: bashir_qau@yahoo.com

Rahmat Ali Khan
Department of Mathematics, Quaid-i-Azam University
Islamabad, Pakistan
e-mail: rahmat_alipk@yahoo.com

Paul W. Eloe
Department of Mathematics, University of Dayton
Dayton, OH 45469-2316, USA
e-mail: Paul.Eloe@notes.udayton.edu

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