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.

Show me the
PDF file (209K),
TEX file, and other files for this article.

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

Return to the EJDE web page