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

Rahmat A. Khan; Bashir Ahmad

Archivum Mathematicum (2005)

  • Volume: 041, Issue: 2, page 135-143
  • ISSN: 0044-8753

Abstract

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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 2 ) .

How to cite

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Khan, 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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  1. Lakshmikantham V., An extension of the method of quasilinearization, J. Optim. Theory Appl. 82 (1994), 315–321. (1994) Zbl0806.34013MR1286689
  2. Lakshmikantham V., Further improvement of generalized quasilinearization, Nonlinear Anal. 27 (1996), 315–321. (1996) Zbl0855.34012MR1389479
  3. Lakshmikantham V., Vatsala A. S., Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, Dordrecht (1998). (1998) Zbl0997.34501MR1640601
  4. 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
  5. 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
  6. 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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