| Title:
|
Approximate solution of an inhomogeneous abstract differential equation (English) |
| Author:
|
Vitásek, Emil |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
31-41 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Recently, we have developed the necessary and sufficient conditions under which a rational function $F(hA)$ approximates the semigroup of operators $\exp (tA)$ generated by an infinitesimal operator $A$. The present paper extends these results to an inhomogeneous equation $u'(t)=Au(t)+f(t)$. (English) |
| Keyword:
|
abstract differential equations |
| Keyword:
|
semigroups of operators |
| Keyword:
|
rational approximations |
| Keyword:
|
A-stability |
| MSC:
|
34A45 |
| MSC:
|
34G10 |
| MSC:
|
34K30 |
| MSC:
|
35K90 |
| MSC:
|
41A20 |
| MSC:
|
47D03 |
| idZBL:
|
Zbl 1249.34169 |
| idMR:
|
MR2891304 |
| DOI:
|
10.1007/s10492-012-0003-1 |
| . |
| Date available:
|
2012-01-09T19:23:52Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141817 |
| . |
| Reference:
|
[1] Dunford, N., Schwartz, J. T.: Linear Operators. 1. General Theory.Interscience Publishers New York-London (1958). MR 0117523 |
| Reference:
|
[2] Kato, T.: Perturbation Theory for Linear Operators.Springer Berlin-Heidelberg-New York (1966). Zbl 0148.12601, MR 0203473 |
| Reference:
|
[3] Práger, M., Taufer, J., Vitásek, E.: Overimplicit multistep methods.Apl. Math. 18 (1973), 399-421. MR 0366041 |
| Reference:
|
[4] Taylor, A. E.: Introduction to Functional Analysis.John Wiley & Sons New York (1958). Zbl 0081.10202, MR 0098966 |
| Reference:
|
[5] Vitásek, E.: Approximate solutions of abstract differential equations.Appl. Math. 52 (2007), 171-183. Zbl 1164.34457, MR 2305871, 10.1007/s10492-007-0008-3 |
| Reference:
|
[6] Yosida, K.: Functional Analysis.Springer Berlin-Heidelberg-New York (1971). Zbl 0217.16001 |
| . |
