Extension of the G -stability concept to the class of the linear multistep block methods

Reiner Vanselow

Aplikace matematiky (1983)

  • Volume: 28, Issue: 1, page 9-20
  • ISSN: 0862-7940

Abstract

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In der vorliegenden Arbeit wird der G -Stabilitätsbegriff von Dahlquist, der die Grundlage für Stabilitätsuntersuchungen bei linearen Mehrschrittverfahren zur Lösung nichtlinearet Anfangswertaufgaben bildet, auf die Klasse der linearen Mehrschrittblockverfahren übertragen. Es wird nachgewiesen, das Blockverfahren, die in diesem Sinne stabil sind, höchstens die Konsistenzordnung 2 haben können.

How to cite

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Vanselow, Reiner. "Erweiterung des $G$-Stabilitätsbegriffes auf die Klasse der linearen Mehrschrittblockverfahren.." Aplikace matematiky 28.1 (1983): 9-20. <http://eudml.org/doc/15270>.

@article{Vanselow1983,
author = {Vanselow, Reiner},
journal = {Aplikace matematiky},
keywords = {$G$-stability; linear multistep; block methods; order of consistency; nonlinear problems; G-stability; linear multistep; block methods; order of consistency; nonlinear problems},
language = {ger},
number = {1},
pages = {9-20},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Erweiterung des $G$-Stabilitätsbegriffes auf die Klasse der linearen Mehrschrittblockverfahren.},
url = {http://eudml.org/doc/15270},
volume = {28},
year = {1983},
}

TY - JOUR
AU - Vanselow, Reiner
TI - Erweiterung des $G$-Stabilitätsbegriffes auf die Klasse der linearen Mehrschrittblockverfahren.
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 1
SP - 9
EP - 20
LA - ger
KW - $G$-stability; linear multistep; block methods; order of consistency; nonlinear problems; G-stability; linear multistep; block methods; order of consistency; nonlinear problems
UR - http://eudml.org/doc/15270
ER -

References

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  1. G. G. Dahlquist, 10.1007/BF01963532, BIT 3 (1963), 27-43. (1963) Zbl0123.11703MR0170477DOI10.1007/BF01963532
  2. G. G. Dahlquist, On stability and error analysis for stiff non-linear problems, Part I, Report TRITA-NA-7508, 1975. (1975) 
  3. G. G. Dahlquist, Error analysis for a class of methods for stiff non-linear initial value problems, Pro. Conf. Numerical Analysis, Dundee 1975, Springer Lecture Notes in Mathematics, 506 (1975), 60-74. (1975) Zbl0352.65042MR0448898
  4. G. G. Dahlquist, On the relation of G-stability to other stability concepts for linear multistep methods, Topics in Numerical Analysis III, 67-80, ed. J. H. Miller, Acad. Press, London, 1977. (1977) Zbl0438.65073
  5. G. G. Dahlquist, G-stability is equivalent to A-stability, Report TRITA-NA-7805, 1978. (1978) Zbl0413.65057
  6. M. Práger J. Taufer E. Vitásek, Overimplicit methods for the solution of evolution problems, Acta Universitatis Carolinae - Mathematica et Physica 1 - 2 (1974), 125-133. (1974) Zbl0342.65052MR0391515
  7. M. Práger J. Taufer E. Vitásek, Overimplicit multistep methods, Apl. mat. 18 (1973), 399-421. (1973) Zbl0298.65052MR0366041
  8. H. A. Watts, A-stable block implicit one-step methods, Sandia Laboratories, Albuquerque, Applied Mathematics, 1971. (1971) Zbl0253.65045
  9. H. A. Watts L. F. Shampine, 10.1007/BF01932819, BIT 12 (1972), 252-266. (1972) Zbl0253.65045MR0307483DOI10.1007/BF01932819
  10. R. Vanselow, Stabilitäts- und Fehleruntersuchungen bei numerischen Verfahren zur Lösung steifer nichtlinearer Anfangswertprobleme, Diplomarbeit, TU Dresden, 1978/79. (1978) 
  11. R. Vanselow, Explizite Konstruktion von linearen Mehrschrittblockverfahren, Apl. Mat. 28 (1983), 1-8. (1983) Zbl0516.65059MR0684706

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