| Title:
|
An extension of the method of quasilinearization (English) |
| Author:
|
Jankowski, Tadeusz |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
201-208 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The method of quasilinearization is a well–known technique for obtaining approximate solutions of nonlinear differential equations. This method has recently been generalized and extended using less restrictive assumptions so as to apply to a larger class of differential equations. In this paper, we use this technique to nonlinear differential problems. (English) |
| Keyword:
|
quasilinearization |
| Keyword:
|
monotone iterations |
| Keyword:
|
quadratic convergence |
| MSC:
|
34A12 |
| MSC:
|
34A45 |
| idZBL:
|
Zbl 1116.34304 |
| idMR:
|
MR2010721 |
| . |
| Date available:
|
2008-06-06T22:41:50Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107867 |
| . |
| Reference:
|
[1] Bellman, R.: Methods of Nonlinear Analysis.Vol. II, Academic Press, New York 1973. Zbl 0265.34002, MR 0381408 |
| Reference:
|
[2] Bellman, R. and Kalaba, R.: Quasilinearization and Nonlinear Boundary Value Problems.American Elsevier, New York 1965. MR 0178571 |
| Reference:
|
[3] Jankowski, T. and Lakshmikantham, V.: Monotone iterations for differential equations with a parameter.J. Appl. Math. Stoch. Anal. 10 (1997), 273–278. MR 1468122 |
| Reference:
|
[4] Jankowski, T. and McRae, F. A.: An extension of the method of quasilinearization for differential problems with a parameter.Nonlinear Stud. 6 (1999), 21–44. MR 1691903 |
| Reference:
|
[5] Ladde, G. S., Lakshmikantham, V. and Vatsala, A. S.: Monotone Iterative Techniques for Nonlinear Differential Equations.Pitman 1985. MR 0855240 |
| Reference:
|
[6] Lakshmikantham, V. and Malek, S.: Generalized quasilenearization.Nonlinear World 1 (1994), 59–63. MR 1282859 |
| Reference:
|
[7] Lakshmikantham, V., Leela, S. and Sivasundaram, S.: Extensions of the Method of Quasilinearization.J. Optimization Theory Appl. Vol. 87 (1995), 379–401. MR 1358749 |
| Reference:
|
[8] Lakshmikantham, V. and Vatsala, A. S.: Generalized Quasilinearization for Nonlinear Problems.Kluwer Academic Publishers, Dordrecht 1998. MR 1640601 |
| Reference:
|
[9] Lakshmikantham, V., Leela, S. and McRae, F. A.: Improved Generalized Quasilinearization Method.Nonlinear Analysis 24 (1995), 1627–1637. MR 1328588 |
| Reference:
|
[10] Lakshmikantham, V. and Shahzad, N.: Further Generalization of Generalized Quasilinearization Method.J. Appl. Math. Stoch. Anal. 7 (1994), 545–552. MR 1310927 |
| Reference:
|
[11] Shahzad, N. and Vatsala, A. S.: An Extension of the Method of Generalized Quasilinearization for Second Order Boundary Value Problems.Appl. Anal. 58 (1995), 77–83. MR 1384590 |
| . |
