| Title:
|
On a differential-algebraic problem (English) |
| Author:
|
Dabrowicz-Tlałka, Anita |
| Author:
|
Jankowski, Tadeusz |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
205-215 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem. (English) |
| Keyword:
|
differential-algebraic problem |
| Keyword:
|
monotone sequences |
| Keyword:
|
quadratic convergence |
| MSC:
|
34A09 |
| MSC:
|
34A34 |
| MSC:
|
34A45 |
| MSC:
|
34B99 |
| idZBL:
|
Zbl 1058.34005 |
| idMR:
|
MR1757241 |
| DOI:
|
10.1023/A:1023018911566 |
| . |
| Date available:
|
2009-09-22T18:03:27Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134435 |
| . |
| Reference:
|
[1] J. Bahi, E. Griepentrog and J. C. Miellou: Parallel treatment of a class of differential-algebraic systems.SIAM J. Numer. Anal. 33 (1996), 1969–1980. MR 1411858, 10.1137/S0036142993258105 |
| Reference:
|
[2] R. Bellman, R. Kalaba: Quasilinearization and Nonlinear Boundary Value Problems.American Elsevier, New York, 1965. MR 0178571 |
| Reference:
|
[3] Z. Jackiewicz, M. Kwapisz: Convergence of waveform relaxation methods for differential-algebraic systems.SIAM J. Numer. Anal. 33 (1996), 2303–2317. MR 1427465, 10.1137/S0036142992233098 |
| Reference:
|
[4] T. Jankowski, V. Lakshmikantham: Monotone iterations for differential eguations with a parameter.J. Appl. Math. Stoch. Anal. 10 (1997), 273–278. MR 1468122, 10.1155/S1048953397000348 |
| Reference:
|
[5] T. Jankowski, M. Kwapisz: Convergence of numerical methods for systems of neutral functional-differential-algebraic eguations.Appl. Math. 40 (1995), 457–472. MR 1353973 |
| Reference:
|
[6] M. Kwapisz: On solving systems of differential algebraic eguations.Appl. Math. 37 (1992), 257–264. MR 1180604 |
| Reference:
|
[7] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala: Monotone Iterative Techniques for Nonlinear Differential Equations.Pitman, Boston, 1985. MR 0855240 |
| . |
