| Title:
|
Unconditional stability of difference formulas (English) |
| Author:
|
Roubíček, Tomáš |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
2 |
| Year:
|
1983 |
| Pages:
|
81-90 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper concerns the solution of partial differential equations of evolution type by the finite difference method. The author discusses the general assumptions on the original equation as well as its discretization, which guarantee that the difference scheme is unconditionally stable, i.e. stable without any stability condition for the time-step. A new notion of the $A_n$-acceptability of the integration formula is introduced and examples of such formulas are given. The results can be applied to ordinary differential equations as well. (English) |
| Keyword:
|
unconditional stability |
| Keyword:
|
complex Banach space |
| Keyword:
|
finite difference method |
| Keyword:
|
$k$-step formula |
| MSC:
|
34G10 |
| MSC:
|
35G10 |
| MSC:
|
35K25 |
| MSC:
|
65J10 |
| MSC:
|
65L05 |
| MSC:
|
65M10 |
| MSC:
|
65N12 |
| idZBL:
|
Zbl 0538.65032 |
| idMR:
|
MR0695181 |
| DOI:
|
10.21136/AM.1983.104008 |
| . |
| Date available:
|
2008-05-20T18:21:18Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104008 |
| . |
| Reference:
|
[1] I. Babuška M.Práger, E. Vitásek: Numerical Processes in Differential Equations.SNTL, Prague, 1966. Zbl 0156.16003, MR 0223101 |
| Reference:
|
[2] B. L. Ehle: A-stable Methods and Pade Approximations to the Exponential.SIAM J. Math. Anal., Vol. 4 (1973), No. 4, pp. 671-680. Zbl 0236.65016, MR 0331787, 10.1137/0504057 |
| Reference:
|
[3] A. Iserles: On the A-acceptability of Pade Approximations.SIAM J. Math. Anal., Vol. 10 (1979), No. 5, pp. 1002-1007. Zbl 0441.41010, MR 0541096, 10.1137/0510091 |
| Reference:
|
[4] E. Hille, R. S. Phillips: Functional Analysis and Semi-groups.Amer. Math. Soc., Vol. 31., rev. ed., Waverly Press, Baltimore, 1957. MR 0089373 |
| . |
