| Title:
|
Functional differential equations (English) |
| Author:
|
Jankowski, Tadeusz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
553-563 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. In this paper we apply this technique to functional differential problems. It is shown that linear iterations converge to the unique solution and this convergence is superlinear. (English) |
| Keyword:
|
quasilinearization |
| Keyword:
|
monotone iterations |
| Keyword:
|
superlinear convergence |
| MSC:
|
34A45 |
| MSC:
|
34K05 |
| MSC:
|
34K07 |
| MSC:
|
34K28 |
| idZBL:
|
Zbl 1023.34070 |
| idMR:
|
MR1923261 |
| . |
| Date available:
|
2009-09-24T10:54:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127743 |
| . |
| Reference:
|
[1] R. Bellman: Methods of Nonlinear Analysis, Vol. I.Academic Press, New York, 1973. MR 0381408 |
| Reference:
|
[2] R. Bellman and R. Kalaba: Quasilinearization and Nonlinear Boundary Value Problems.American Elsevier, New York, 1965. MR 0178571 |
| Reference:
|
[3] J. K. Hale and S. M. V. Lunel: Introduction to Functional Differential Equations.Springer-Verlag, New York, Berlin, 1993. MR 1243878 |
| Reference:
|
[4] T. Jankowski and F. A. McRae: An extension of the method of quasilinearization for differential problems with a parameter.Nonlinear Stud. 6 (1999), 21–44. MR 1691903 |
| Reference:
|
[5] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala: Monotone Iterative Techniques for Nonlinear Differential Equations.Pitman, Boston, 1985. MR 0855240 |
| Reference:
|
[6] 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:
|
[7] V. Lakshmikantham and A. S. Vatsala: Generalized Quasilinearization for Nonlinear Problems.Kluwer Academic Publishers, Dordrecht-Boston-London, 1998. MR 1640601 |
| . |
