| Title:
|
Convergence of multistep methods for systems of ordinary differential equations with parameters (English) |
| Author:
|
Jankowski, Tadeusz |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1987 |
| Pages:
|
257-270 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The author considers the convergence of quasilinear nonstationary multistep methods for systems of ordinary differential with parameters. Sufficient conditions for their convergence are given. The new numerical method is tested for two examples and it turns out to be a little better than the Hamming method. (English) |
| Keyword:
|
quasilinear nonstationary multistep methods |
| Keyword:
|
convergence |
| Keyword:
|
Hamming method |
| MSC:
|
34B15 |
| MSC:
|
65L10 |
| idZBL:
|
Zbl 0634.65063 |
| idMR:
|
MR0897830 |
| DOI:
|
10.21136/AM.1987.104257 |
| . |
| Date available:
|
2008-05-20T18:32:33Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104257 |
| . |
| Reference:
|
[1] I. Babuška M. Práger E. Vitásek: Numerical processes in differential equations.Praha 1966. MR 0223101 |
| Reference:
|
[2] R. Conti: Problèmes iinéaires pour les équations différentielles ordinaires.Mathematische Nachrichten 23 (1961), 161-178. MR 0138818, 10.1002/mana.1961.3210230304 |
| Reference:
|
[3] A. Gasparini A. Mangini: Sul calcolo numerico delle soluzioni di un noto problema ai limiti per l'equazione $y'=\lambda f(x,y)$.Le Matematiche 22 (1965), 101-121. MR 0191098 |
| Reference:
|
[4] R. W. Hamming: Stable predictor-corrector methods for ordinary differential equations.Journal of the Association for Computing Machinery, t. 6 nr. 1 (1959), 37-47. Zbl 0086.11201, MR 0102179, 10.1145/320954.320958 |
| Reference:
|
[5] 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:
|
[6] K. Jankowska T. Jankowski: On a boundary-value problem of a differential equation with a deviated argument.(Polish), Zeszyty Naukowe Politechniki Gdańskiej, Matematyka 7 (1973), 33-48. |
| Reference:
|
[7] T. Jankowski: On the convergence of multistep methods for ordinary differential equations with discontinuities.Demonstratio Mathematica 16 (1983), 651 - 675. Zbl 0571.65065, MR 0733727, 10.1515/dema-1983-0309 |
| Reference:
|
[8] T. Jankowski M. Kwapisz: On the existence and uniqueness of solutions of boundary-value problem for differential equations with parameter.Mathematische Nachrichten 71 (1976), 237-247. MR 0405190, 10.1002/mana.19760710119 |
| Reference:
|
[9] H. Jeffreys B. S. Jeffreys: Methods of mathematical physics.Cambridge UP 1956. MR 0074466 |
| Reference:
|
[10] A. V. Kibenko A. I. Perov: A two-point boundary value problem with parameter.(Russian), Azerbaidžan. Gos. Univ. Učen. Zap. Ser. Fiz.-Mat. i Him. Nauk 3 (1961), 21-30. MR 0222376 |
| Reference:
|
[11] J. D. Lambert: Computational methods in ordinary differential equations.New York 1973. Zbl 0258.65069, MR 0423815 |
| Reference:
|
[12] D. I. Martiniuk: Lectures on qualitative theory of difference equations.(Russian). Kiev: Naukova Dumka 1972. MR 0611163 |
| Reference:
|
[13] R. Pasquali: Un procedimento di calcolo connesso ad un noto problema ai limiti per l'equazione $x'= f(t, x, \lambda)$.Le Matematiche 23 (1968), 319-328. Zbl 0182.22003, MR 0267785 |
| Reference:
|
[14] Z. B. Seidov: A multipoint boundary value problem with a parameter for systems of differential equations in Banach space.Sibirskij Matematiczeskij Žurnał 9 (1968), 223-228. MR 0281987 |
| Reference:
|
[15] D. Squier: Non-linear difference schemes.Journal of Approximation Theory 1 (1968), 236-242. Zbl 0219.39003, MR 0234637, 10.1016/0021-9045(68)90027-0 |
| Reference:
|
[16] J. Stoer R. Bulirsch: Einführung in die Numerische Mathematik I:.Springer Verlag Berlin Heidelberg 1972. MR 0400617 |
| Reference:
|
[17] S. Takahashi: Die Differentialgleichung $y'= k f(x,y)$.Tôhoku Math. J. 34 (1941), 249-256. |
| . |
