| Title:
|
On numerical integration of implicit ordinary differential equations (English) |
| Author:
|
Jackiewicz, Zdzisław |
| Author:
|
Kwapisz, Marian |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
26 |
| Issue:
|
2 |
| Year:
|
1981 |
| Pages:
|
97-110 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential equations. The convergence theorem is proved and some numerical examples are given. (English) |
| Keyword:
|
nonstationary quasilinear multistep methods |
| Keyword:
|
implicit ordinary differential equations |
| Keyword:
|
convergence theorem |
| Keyword:
|
numerical examples |
| MSC:
|
65J15 |
| MSC:
|
65L05 |
| idZBL:
|
Zbl 0469.65058 |
| idMR:
|
MR0612667 |
| DOI:
|
10.21136/AM.1981.103901 |
| . |
| Date available:
|
2008-05-20T18:16:28Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103901 |
| . |
| Reference:
|
[1] W. H. Enright: Second derivative multistep methods for stiff ordinary differential equations.SIAM J. Numer. Anal. 11, (1974), 321-331. MR 0351083, 10.1137/0711029 |
| Reference:
|
[2] P. Hartman: Ordinary Differential Equations.New York-London-Sydney: J. Wiley 1964. Zbl 0125.32102, MR 0171038 |
| Reference:
|
[3] P. Henrici: Discrete Variable Methods in Ordinary Differential Equations.New York: J. Wiley 1968. MR 0135729 |
| Reference:
|
[4] Z. Jackiewicz M. Kwapisz: On the convergence of multistep methods for the Cauchy problem for ordinary differential equations.Computing 20, (1978), 351 - 361. MR 0619909, 10.1007/BF02252383 |
| Reference:
|
[5] M. Kwapisz: On the existence and uniqueness of solutions of a certain integral-functional equation.Ann. Polon. Math. 31, (1975), 23 - 41. MR 0380329, 10.4064/ap-31-1-23-41 |
| Reference:
|
[6] J. D. Lambert: Computational Methods in Ordinary Differential Equations.London-New York: J. Wiley 1973. Zbl 0258.65069, MR 0423815 |
| Reference:
|
[7] L. Lapidus J. H. Seifeld: Numerical Solution of Ordinary Differential Equations.London - New York: Academic Press 1971. MR 0281355 |
| Reference:
|
18] J. D. Mamiedow: Approximate Methods of Solution of Ordinary Differential Equations.(in Russian). Baku: Maarif 1974. |
| Reference:
|
[9] D. I. Martinjuk: Lecture on Qualitative Theory of Difference Equations.(in Russian). Kiev: Naukova Dumka 1972. MR 0611163, 10.1093/comjnl/5.4.329 |
| Reference:
|
[10] H. H. Rosenbrock: Some general implicit processes for the numerical solution of differential equations.Comput. J. 5 (1963), 329-330. Zbl 0112.07805, MR 0155434 |
| . |
