| Title:
|
On numerical solution of ordinary differential equations with discontinuities (English) |
| Author:
|
Jankowski, Tadeusz |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
6 |
| Year:
|
1988 |
| Pages:
|
487-492 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The author defines the numerical solution of a first order ordinary differential equation on a bounded interval in the way covering the general form of the so called one-step methods, proves convergence of the method (without the assumption of continuity of the righthad side) and gives a sufficient condition for the order of convergence to be $O(h^v)$. (English) |
| Keyword:
|
discontinuities |
| Keyword:
|
system |
| Keyword:
|
one-step method |
| Keyword:
|
convergence |
| Keyword:
|
order of convergence |
| Keyword:
|
numerical solution of differential equations |
| MSC:
|
34A34 |
| MSC:
|
65L05 |
| idZBL:
|
Zbl 0671.65061 |
| idMR:
|
MR0973242 |
| DOI:
|
10.21136/AM.1988.104326 |
| . |
| Date available:
|
2008-05-20T18:35:40Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104326 |
| . |
| Reference:
|
[1] I. Babuška M. Práger E. Vitásek: Numerical processes in differential equations.SNTL, Praha 1966. MR 0223101 |
| Reference:
|
[2] B. A. Chartres R. S. Stepleman: Actual order of convergence of Runge-Kutta methods on differential equations with discontinuities.SIAM J. Numer. Anal. 11 (1974), 1193-1206. MR 0381316, 10.1137/0711090 |
| Reference:
|
[3] E. A. Coddington N. Levinson: Theory of ordinary differential equations.Mc Graw-Hill, New York 1955. MR 0069338 |
| Reference:
|
[4] A. Feldstein R. Goodman: Numerical solution of ordinary and retardea differential equations with discontinuous derivatives.Numer. Math. 21 (1973), 1-13. MR 0381320, 10.1007/BF01436181 |
| Reference:
|
[5] P. Henrici: Discrete variable methods in ordinary differential equations.J. Wiley, New York 1968. MR 0135729 |
| Reference:
|
[6] T. Jankowski: Some remarks on numerical solution of initial problems for systems of differential equations.Apl. Mat. 24 (1979), 421 - 426. Zbl 0447.65039, MR 0547045 |
| Reference:
|
[7] T. Jankowski: On the convergence of multistep methods for ordinary differential equations with discontinuities.Demostratio Math. 16 (1983), 651 - 675. Zbl 0571.65065, MR 0733727 |
| Reference:
|
[8] D. P. Squier: One-step methods for ordinary differential equations.Numer. Math. 13 (1969), 176-179. Zbl 0182.21901, MR 0247773, 10.1007/BF02163235 |
| Reference:
|
[9] J. Szarski: Differential inequalities.PWN- Polish. Scient. Publ., Warsaw 1967. Zbl 0177.39203 |
| . |
