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

Rahmat A. Khan, Bashir Ahmad

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

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.