A note on rapid convergence of approximate solutions for second order periodic boundary value problems
Archivum Mathematicum (2005)
- Volume: 041, Issue: 2, page 135-143
- ISSN: 0044-8753
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topKhan, Rahmat A., and Ahmad, Bashir. "A note on rapid convergence of approximate solutions for second order periodic boundary value problems." Archivum Mathematicum 041.2 (2005): 135-143. <http://eudml.org/doc/249487>.
@article{Khan2005,
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$$(k\ge 2)$.},
author = {Khan, Rahmat A., Ahmad, Bashir},
journal = {Archivum Mathematicum},
keywords = {generalized quasilinearization; periodic boundary value problems; rapid convergence; generalized quasilinearization},
language = {eng},
number = {2},
pages = {135-143},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A note on rapid convergence of approximate solutions for second order periodic boundary value problems},
url = {http://eudml.org/doc/249487},
volume = {041},
year = {2005},
}
TY - JOUR
AU - Khan, Rahmat A.
AU - Ahmad, Bashir
TI - A note on rapid convergence of approximate solutions for second order periodic boundary value problems
JO - Archivum Mathematicum
PY - 2005
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 041
IS - 2
SP - 135
EP - 143
AB - In this paper, we develop a generalized quasilinearization technique for a nonlinear second order periodic boundary value problem and obtain a sequence of approximate solutions converging uniformly and quadratically to a solution of the problem. Then we improve the convergence of the sequence of approximate solutions by establishing the convergence of order $k$$(k\ge 2)$.
LA - eng
KW - generalized quasilinearization; periodic boundary value problems; rapid convergence; generalized quasilinearization
UR - http://eudml.org/doc/249487
ER -
References
top- Lakshmikantham V., An extension of the method of quasilinearization, J. Optim. Theory Appl. 82 (1994), 315–321. (1994) Zbl0806.34013MR1286689
- Lakshmikantham V., Further improvement of generalized quasilinearization, Nonlinear Anal. 27 (1996), 315–321. (1996) Zbl0855.34012MR1389479
- Lakshmikantham V., Vatsala A. S., Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, Dordrecht (1998). (1998) Zbl0997.34501MR1640601
- Nieto J. J., Generalized quasilinearization method for a second order differential equation with Dirichlet boundary conditions, Proc. Amer. Math. Soc. 125 (1997), 2599–2604. (1997) MR1402880
- Cabada A., Nieto J. J., Pita-da-Veige R., A note on rapid convergence of approximate solutions for an ordinary Dirichlet problem, Dynam. Contin. Discrete Impuls. Systems 4 (1998), 23–30. (1998) MR1606766
- Mohapatra R. N., Vajravelu K., Yin Y., Generalized quasilinearization method for second order boundary value problems, Nonlinear Anal. 36 (1999), 799–806. (1999) Zbl0922.34018MR1680293
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