| Title:
|
Boundary value problems for ODEs (English) |
| Author:
|
Jankowski, Tadeusz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
743-756 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We use the method of quasilinearization to boundary value problems of ordinary differential equations showing that the corresponding monotone iterations converge to the unique solution of our problem and this convergence is quadratic. (English) |
| Keyword:
|
quasilinearization |
| Keyword:
|
monotone iterations |
| Keyword:
|
quadratic convergence |
| MSC:
|
34A45 |
| MSC:
|
34B05 |
| MSC:
|
34B08 |
| MSC:
|
34B15 |
| MSC:
|
34B99 |
| idZBL:
|
Zbl 1080.34511 |
| idMR:
|
MR2000066 |
| . |
| Date available:
|
2009-09-24T11:06:11Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127836 |
| . |
| Reference:
|
[1] R. Bellman: Methods of Nonlinear Analysis, Vol. II.Academic Press, New York, 1973. Zbl 0265.34002, MR 0381408 |
| Reference:
|
[2] R. Bellman and R. Kalaba: Quasilinearization and Nonlinear Boundary Value Problems.American Elsevier, New York, 1965. MR 0178571 |
| Reference:
|
[3] G. S. Ladde V. Lakshmikantham and A. S. Vatsala: Monotone Iterative Techniques for Nonlinear Differential Equations.Pitman, Boston, 1985. MR 0855240 |
| Reference:
|
[4] V. Lakshmikantham: Further improvements of generalized quasilinearization method.Nonlinear Anal. 27 (1996), 223–227. MR 1389479, 10.1016/0362-546X(94)00281-L |
| Reference:
|
[5] V. Lakshmikantham, S. Leela and S. Sivasundaram: Extensions of the method of quasilinearization.J. Optim. Theory Appl. 87 (1995), 379–401. MR 1358749, 10.1007/BF02192570 |
| Reference:
|
[6] V. Lakshmikantham, N. Shahzad and J. J. Nieto: Methods of generalized quasilinearization for periodic boundary value problems.Nonlinear Anal. 27 (1996), 143–151. MR 1389474, 10.1016/0362-546X(95)00021-M |
| Reference:
|
[7] V. Lakshmikantham and N. Shahzad: Further generalization of generalized quasilinearization method.J. Appl. Math. Stoch. Anal. 7 (1994), 545–552. MR 1310927, 10.1155/S1048953394000420 |
| Reference:
|
[8] V. Lakshmikantham and A. S. Vatsala: Generalized Quasilinearization for Nonlinear Problems.Kluwer Academic Publishers, Dordrecht, Boston, London, 1998. MR 1640601 |
| Reference:
|
[9] Y. Yin: Remarks on first order differential equations with anti-periodic boundary conditions.Nonlinear Times Digest 2 (1995), 83–94. Zbl 0832.34018, MR 1333336 |
| . |
