| Title:
|
Global error estimation in the numerical solution of retarded differential equations by Euler's method (English) |
| Author:
|
Jackiewicz, Zdzisław |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
3 |
| Year:
|
1983 |
| Pages:
|
177-185 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper Zadunaisky's technique is used to estimate the global error propagated in the numerical solution of the system of retarded differential equations by Euler's method. Some numerical examples are given. (English) |
| Keyword:
|
global error estimation |
| Keyword:
|
retarded differential equations |
| Keyword:
|
Euler’s method |
| Keyword:
|
system of ordinary differential equations |
| Keyword:
|
numerical examples |
| MSC:
|
34K05 |
| MSC:
|
34K99 |
| MSC:
|
65L05 |
| idZBL:
|
Zbl 0536.65063 |
| idMR:
|
MR0701737 |
| DOI:
|
10.21136/AM.1983.104024 |
| . |
| Date available:
|
2008-05-20T18:22:04Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104024 |
| . |
| Reference:
|
[1] R. E. Bellman J. O. Buell R. E. Kalaba: Numerical integration of a differential-difference equation with a decreasing time-lag.Comm. ACM 8 (1965), 227-228. MR 0176628, 10.1145/363831.364879 |
| Reference:
|
[2] R. Frank: Schatzungen des Globalen Diskretisierungsfehlers bei Runge-Kutte Methoden.ISNM 27, pp. 95-70. Basel, Stuttgart: Birkhäuser (1975). MR 0411172 |
| Reference:
|
[3] R. Frank C. W. Ueberhuber: Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations.BIT 17 (1977), 146-159. MR 0488748, 10.1007/BF01932286 |
| Reference:
|
[4] D. R. Hill: A new class of one-step methods for the solution of Volterra functional differential equations.BIT 14 (1974), 298-305. Zbl 0293.65047, MR 0386311, 10.1007/BF01933229 |
| Reference:
|
[5] Z. Jackiewicz: Convergence of multistep methods for Volterra functional differential equations.Numer. Math. 32 (1979), 307-332. Zbl 0388.65028, MR 0535197, 10.1007/BF01397004 |
| Reference:
|
[6] Z. Jackiewicz: Global error estimation in the numerical solution of integro-differential equations by Euler's method.To appear in Zastos. Mat. Zbl 0557.65094, MR 0757894 |
| Reference:
|
[7] H. J. Stetter: Economical global error estimation.In: Proceedings of Symposium on Stiff Differential Systems, Wildbad, 1973. New York: Plenum Publ. Co. 1974. MR 0405863 |
| Reference:
|
[8] P. E. Zadunaisky: On the estimation of errors propagated in the numerical integration of of ordinary differential equations.Numer. Math. 27 (1976), 21 - 39. MR 0431696, 10.1007/BF01399082 |
| . |
