Address.
Department of Mathematics, Quaid-i-Azam
University,
Islamabad, Pakistan
Department of Mathematics, Faculty of Science
King Abdul Aziz University, P. O. Box 80203, Jeddah-21589, Saudi Arabia
E-mail. bashir_qau@yahoo.com
Abstract.
In this paper, we develop a generalized quasilinearization technique for a
nonlinear second order periodic boundary value problem and obtain
a sequence of approximate solutions converging uniformly and
quadratically to a solution of the problem. Then we improve the
convergence of the sequence of approximate solutions by
establishing the convergence of order $k$ $(k\geq
2)$.
AMSclassification. 34A37, 34C25.
Keywords. Generalized quasilinearization, periodic boundary value problems, rapid convergence.