| Title:
|
A note on rapid convergence of approximate solutions for second order periodic boundary value problems (English) |
| Author:
|
Khan, Rahmat A. |
| Author:
|
Ahmad, Bashir |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
135-143 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $k$ $(k\ge 2)$. (English) |
| Keyword:
|
generalized quasilinearization |
| Keyword:
|
periodic boundary value problems |
| Keyword:
|
rapid convergence |
| MSC:
|
34A45 |
| MSC:
|
34B15 |
| MSC:
|
34C25 |
| idZBL:
|
Zbl 1117.34018 |
| idMR:
|
MR2164662 |
| . |
| Date available:
|
2008-06-06T22:45:29Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107943 |
| . |
| Reference:
|
[1] Lakshmikantham V.: An extension of the method of quasilinearization.J. Optim. Theory Appl. 82 (1994), 315–321. Zbl 0806.34013, MR 1286689 |
| Reference:
|
[2] Lakshmikantham V.: Further improvement of generalized quasilinearization.Nonlinear Anal. 27 (1996), 315–321. Zbl 0855.34012, MR 1389479 |
| Reference:
|
[3] Lakshmikantham V., Vatsala A. S.: Generalized Quasilinearization for Nonlinear Problems.Kluwer Academic Publishers, Dordrecht (1998). Zbl 0997.34501, MR 1640601 |
| Reference:
|
[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. MR 1402880 |
| Reference:
|
[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. MR 1606766 |
| Reference:
|
[6] Mohapatra R. N., Vajravelu K., Yin Y.: Generalized quasilinearization method for second order boundary value problems.Nonlinear Anal. 36 (1999), 799–806. Zbl 0922.34018, MR 1680293 |
| . |
