| Title:
|
One-step methods for ordinary differential equations with parameters (English) |
| Author:
|
Jankowski, Tadeusz |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1990 |
| Pages:
|
67-83 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we are concerned with the problem of numerical solution of ordinary differential equations with parameters. Our method is based on a one-step procedure for IDEs combined with an iterative process. Simple sufficient conditions for the convergence of this method are obtained. Estimations of errors and some numerical examples are given. (English) |
| Keyword:
|
ordinary differential equations with parameters |
| Keyword:
|
numerical solution |
| Keyword:
|
one-step method |
| Keyword:
|
parameter estimation |
| Keyword:
|
iterative methods |
| Keyword:
|
convergence |
| Keyword:
|
error estimates |
| Keyword:
|
numerical examples |
| MSC:
|
34B15 |
| MSC:
|
65L06 |
| MSC:
|
65L10 |
| MSC:
|
65L15 |
| MSC:
|
65L70 |
| idZBL:
|
Zbl 0701.65053 |
| idMR:
|
MR1039412 |
| DOI:
|
10.21136/AM.1990.104388 |
| . |
| Date available:
|
2008-05-20T18:38:29Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104388 |
| . |
| Reference:
|
[1] I. Babuška M. Práger E. Vitásek: Numerical processes in differential equations.Praha 1966. MR 0223101 |
| Reference:
|
[2] R. Conti: Problemes lineaires pour les équations differentialles ordinaires.Math. Nachr. 23 (1961), 161-178. MR 0138818, 10.1002/mana.1961.3210230304 |
| Reference:
|
[3] J. W. Daniel R. E. Moore: Computation and theory in ordinary differential equations.San Francisco 1970. MR 0267765 |
| Reference:
|
[4] 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:
|
[5] P. Henrici: Discrete variable methods in ordinary differential equations.John Wiley, New York 1962. Zbl 0112.34901, MR 0135729 |
| Reference:
|
[6] T. Jankowski M. Kwapisz: On the existence and uniqueness of solutions of boundary-value problem for differential equations with parameter.Math. Nachr. 71 (1976), 237-247. MR 0405190, 10.1002/mana.19760710119 |
| Reference:
|
[7] H. B. Keller: Numerical methods for two-point boundary-value problems.Blaisdell, London 1968. Zbl 0172.19503, MR 0230476 |
| Reference:
|
[8] A. V. Kibenko A. I. Perov: A two-point boundary value problem with parameter.(Russian), Azerbaidzan. Gos. Univ. Učen. Zap. Ser. Fiz.-Mat. i Him. Nauka 3 (1961), 21 - 30. MR 0222376 |
| Reference:
|
[9] J. Lambert: Computational methods in ordinary differential equations.London 1973. Zbl 0258.65069, MR 0423815 |
| Reference:
|
[10] A. 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:
|
[11] Z. B. Seidov: A multipoint boundary value problem with a parameter for systems of differential equations in Banach space.(Russian). Sibirski Math. Z. 9 (1968), 223 - 228. MR 0281987 |
| Reference:
|
[12] J. Stoer R. Bulirsch: Introduction to numerical analysis.New York, Heidelberg, Berlin 1980. MR 0578346 |
| Reference:
|
[13] H. J. Stetter: Analysis of discretization methods for ordinary differential equations.New York, Heidelberg, Berlin 1973. Zbl 0276.65001, MR 0426438 |
| Reference:
|
[14] K. Zawischa: Über die Differentialgleichung $y' = kf(x,y)$ deren Lösungskurve durch zwei gegebene Punkte hindurchgehen soll.Monatsh. Math. Phys. 37 (1930), 103-124. MR 1549778, 10.1007/BF01696760 |
| . |
