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On the stability of backward differentiation methods. (English) Zbl 0483.65045


MSC:

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

Software:

DIFSUB
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Full Text: DOI EuDML

References:

[1] Brayton, R.K., Gustavson, F.G., Hachtel, J.D.: A new efficient algorithm for solving differential-algebraic systems using implicit backward differentiation formulae. Proc. IEEE60, 98-108 (1972) · doi:10.1109/PROC.1972.8562
[2] Brayton, R.K., Conley, C.C.: Some results on the stability and instability of the backward differentiation methods with non-uniform time steps. In: Topics in Numerical Analysis (J.J. Miller, ed.). Proc. of the Royal Irish Academy. London: Academic Press 1973 · Zbl 0298.65053
[3] Curtiss, C.F., Hirschfelder, J.O.: Integration of stiff equations. Proc. Nat. Acad. Sci. U.S.A.38, 235-243 (1952) · Zbl 0046.13602 · doi:10.1073/pnas.38.3.235
[4] Dahlquist, G.: Error analysis for a class of methods for stiff non-linear initial value problems. In: Proc. Conf. Numer. Analysis Dundee 1975, Lecture Notes in Mathematics, Vol. 506, pp. 60-74. Berlin-Heidelberg-New York: Springer 1976
[5] Fried, I.: Numerical Solution of Differential Equations. New York-London: Academic Press 1979 · Zbl 0464.65057
[6] Gear, C.W.: The automatic integration of ordinary differential equations. Comm. ACM14, 176-179 (1971) · Zbl 0217.21701 · doi:10.1145/362566.362571
[7] Gear, C.W.: Algorithm 407, DIFSUB for solution of ordinary differential equations. Comm. ACM14, 185-190 (1971) · doi:10.1145/362566.362573
[8] Gekeler, E.: A-priori error estimates of Galerkin backward differentiation methods in time-inhomogeneous parabolic problems. Numer. Math.30, 369-383 (1978) · Zbl 0368.65049 · doi:10.1007/BF01398506
[9] Lambert, J.D.: Computational Methods in Ordinary Differential Equations, New York: John Wiley 1973 · Zbl 0258.65069
[10] LeRoux, M.-N.: Semi-discretisation en temps pour les equations d’evolution paraboliques lorsque l’operateur depend du temps. R.A.I.R.O.13, 119-137 (1979) · Zbl 0413.65066
[11] Nevanlinna, O.: On error bounds forG-stable methods. BIT16, 79-84 (1976) · Zbl 0321.65044 · doi:10.1007/BF01940780
[12] Stetter, H.J.: Analysis of Discretization Methods for Ordinary Differential Equations. Berlin: Springer-Verlag 1973 · Zbl 0276.65001
[13] Strang, G., Fix, G.J.: An analysis of the finite element method. Englewood Cliffs, N.J.: Prentice-Hall 1973 · Zbl 0356.65096
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