| Title:
|
Approximate solutions of abstract differential equations (English) |
| Author:
|
Vitásek, Emil |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
171-183 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The methods of arbitrarily high orders of accuracy for the solution of an abstract ordinary differential equation are studied. The right-hand side of the differential equation under investigation contains an unbounded operator which is an infinitesimal generator of a strongly continuous semigroup of operators. Necessary and sufficient conditions are found for a rational function to approximate the given semigroup with high accuracy. (English) |
| Keyword:
|
abstract differential equations |
| Keyword:
|
semigroups of operators |
| Keyword:
|
rational approximations |
| Keyword:
|
$A$-stability |
| MSC:
|
34G10 |
| MSC:
|
34K30 |
| MSC:
|
35K90 |
| MSC:
|
47D03 |
| idZBL:
|
Zbl 1164.34457 |
| idMR:
|
MR2305871 |
| DOI:
|
10.1007/s10492-007-0008-3 |
| . |
| Date available:
|
2009-09-22T18:29:04Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134669 |
| . |
| Reference:
|
[1] N. Bourbaki: Fonctions d’une variable réelle (théorie élémentaire).Hermann & Cie, Paris, 1961. (French) Zbl 0131.05001 |
| Reference:
|
[2] J. C. Butcher: The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods.John Wiley & Sons, Chichester, 1987. Zbl 0616.65072, MR 0878564 |
| Reference:
|
[3] N. Dunford, J. Schwartz: Linear Operators, Vol. I.Interscience, New York-London, 1963. MR 0188745 |
| Reference:
|
[4] T. Kato: Perturbation Theory for Linear Operators.Springer-Verlag, Berlin-Heidelberg-New York, 1966. Zbl 0148.12601, MR 0203473 |
| Reference:
|
[5] M. Práger, J. Taufer, E. Vitásek: Overimplicit multistep methods.Apl. Mat. 18 (1973), 399–421. MR 0366041 |
| Reference:
|
[6] K. Yosida: Functional analysis.Springer-Verlag, Berlin-Heidelberg-New York, 1971. Zbl 0217.16001 |
| . |
