# 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

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- 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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