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 $k$ $(k\ge 2)$.
@article{107943,
author = {Rahmat A. Khan and Bashir Ahmad},
title = {A note on rapid convergence of approximate solutions for second order periodic boundary value problems},
journal = {Archivum Mathematicum},
volume = {041},
year = {2005},
pages = {135-143},
zbl = {1117.34018},
mrnumber = {2164662},
language = {en},
url = {http://dml.mathdoc.fr/item/107943}
}
Khan, Rahmat A.; Ahmad, Bashir. A note on rapid convergence of approximate solutions for second order periodic boundary value problems. Archivum Mathematicum, Tome 041 (2005) pp. 135-143. http://gdmltest.u-ga.fr/item/107943/
An extension of the method of quasilinearization, J. Optim. Theory Appl. 82 (1994), 315–321. (1994) | MR 1286689 | Zbl 0806.34013
Further improvement of generalized quasilinearization, Nonlinear Anal. 27 (1996), 315–321. (1996) | MR 1389479 | Zbl 0855.34012
Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, Dordrecht (1998). (1998) | MR 1640601 | Zbl 0997.34501
Generalized quasilinearization method for a second order differential equation with Dirichlet boundary conditions, Proc. Amer. Math. Soc. 125 (1997), 2599–2604. (1997) | MR 1402880
A note on rapid convergence of approximate solutions for an ordinary Dirichlet problem, Dynam. Contin. Discrete Impuls. Systems 4 (1998), 23–30. (1998) | MR 1606766
Generalized quasilinearization method for second order boundary value problems, Nonlinear Anal. 36 (1999), 799–806. (1999) | MR 1680293 | Zbl 0922.34018