Unconditional stability of difference formulas
Aplikace matematiky (1983)
- Volume: 28, Issue: 2, page 81-90
- ISSN: 0862-7940
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topRoubíček, Tomáš. "Unconditional stability of difference formulas." Aplikace matematiky 28.2 (1983): 81-90. <http://eudml.org/doc/15279>.
@article{Roubíček1983,
abstract = {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.},
author = {Roubíček, Tomáš},
journal = {Aplikace matematiky},
keywords = {unconditional stability; complex Banach space; finite difference method; $k$-step formula; unconditional stability; complex Banach space; finite difference method; k-step formula},
language = {eng},
number = {2},
pages = {81-90},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Unconditional stability of difference formulas},
url = {http://eudml.org/doc/15279},
volume = {28},
year = {1983},
}
TY - JOUR
AU - Roubíček, Tomáš
TI - Unconditional stability of difference formulas
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 2
SP - 81
EP - 90
AB - 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.
LA - eng
KW - unconditional stability; complex Banach space; finite difference method; $k$-step formula; unconditional stability; complex Banach space; finite difference method; k-step formula
UR - http://eudml.org/doc/15279
ER -
References
top- I. Babuška M.Práger, E. Vitásek, Numerical Processes in Differential Equations, SNTL, Prague, 1966. (1966) Zbl0156.16003MR0223101
- B. L. Ehle, 10.1137/0504057, SIAM J. Math. Anal., Vol. 4 (1973), No. 4, pp. 671-680. (1973) Zbl0236.65016MR0331787DOI10.1137/0504057
- A. Iserles, 10.1137/0510091, SIAM J. Math. Anal., Vol. 10 (1979), No. 5, pp. 1002-1007. (1979) Zbl0441.41010MR0541096DOI10.1137/0510091
- E. Hille, R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc., Vol. 31., rev. ed., Waverly Press, Baltimore, 1957. (1957) MR0089373
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