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Vanselow, Reiner

Erweiterung des G-Stabilitätsbegriffes auf die Klasse der linearen Mehrschrittblockverfahren. (German) Zbl 0516.65060

Apl. Mat. 28, 9-20 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0516.65060

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems

Keywords:

G-stability; linear multistep; block methods; order of consistency; nonlinear problems
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\textit{R. Vanselow}, Apl. Mat. 28, 9--20 (1983; Zbl 0516.65060)
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References:

[1] G. G. Dahlquist: A special stability problem for linear multistep methods. BIT 3 (1963), 27-43. · Zbl 0123.11703
[2] G. G. Dahlquist: On stability and error analysis for stiff non-linear problems, Part I. Report TRITA-NA-7508, 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.
[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 J. H. Miller, Acad. Press, London, 1977. · Zbl 0438.65073
[5] G. G. Dahlquist: G-stability is equivalent to A-stability. Report TRITA-NA-7805, 1978. · Zbl 0413.65057
[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. · Zbl 0342.65052
[7] M. Práger J. Taufer E. Vitásek: Overimplicit multistep methods. Apl. mat. 18 (1973), 399-421. · Zbl 0298.65052
[8] H. A. Watts: A-stable block implicit one-step methods. Sandia Laboratories, Albuquerque, Applied Mathematics, 1971. · Zbl 0253.65045
[9] H. A. Watts L. F. Shampine: A-stable block implicit one-step methods. BIT 12 (1972), 252-266. · Zbl 0253.65045
[10] R. Vanselow: Stabilitäts- und Fehleruntersuchungen bei numerischen Verfahren zur Lösung steifer nichtlinearer Anfangswertprobleme. Diplomarbeit, TU Dresden, 1978/79.
[11] R. Vanselow: Explizite Konstruktion von linearen Mehrschrittblockverfahren. Apl. Mat. 28 (1983), 1-8. · Zbl 0516.65059
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