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A note on rapid convergence of
approximate solutions
for second order periodic boundary
value problems

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*Rahmat A. Khan, Bashir Ahmad*

**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.