Global dissipativity for a-stable methods

SIAM Journal on Numerical Analysis

Volumn 34, Issue 1, 1997, Pages 119-142

  Hill, A T ^a  

^a UNIVERSITY OF BATH   (United Kingdom)

Author keywords

Dissipativity; G stability; Multistep methods

Indexed keywords

EID: 0000614713     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994270971     Document Type: Article

References (17)

1. C. BAIOCCHI AND M. CROUZEIX, On the equivalence of A-stability and G-stability, Appl. Numer. Math., 5 (1989), pp. 19-22.
2. K. BARRAGE AND J. C. BUTCHER, Stability criteria for implicit Runge-Kutta processes, SIAM J. Numer. Anal., 16 (1979), pp. 1095-1113.
3. J. C. BUTCHER, A stability property of implicit Runge-Kutta methods, BIT, 15 (1975), pp. 358-361.
4. J. B. CONWAY, Functions of One Complex Variable, 2nd ed., Springer-Verlag, Berlin, New York, 1978.
5. G. DAHLQUIST, A special stability problem for linear multistep methods, BIT, 3 (1963), pp. 27-43.
6. G. DAHLQUIST, Error analysis for a class of methods for stiff nonlinear initial value problems, in Numerical Analysis, Dundee 1975, Lecture Notes in Mathematics 506, Springer-Verlag, Berlin, New York, pp. 60-74.
7. G. DAHLQUIST, G-stability is equivalent to A-stability, BIT, 18 (1978), pp, 384-401.
8. T. EIROLA AND O. NEVANLINNA, What do multistep methods approximate? Numer. Math., 53 (1988), pp. 559-569.
9. D. GILBARG AND N. S. TRUDlNGER, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer-Verlag, Berlin, New York, 1983.
10. E. HAIRER AND G. WANNER, Solving Ordinary Differential Equations II, Springer-Verlag, Berlin, New York, 1991.
11. A. T. HILL AND E. SÜLI, Upper semicontinuity of attractors for linear multistep methods approximating sectorial evolution equations, Math. Comp., 64 (1995), pp. 1097-1122.
12. A. R. HUMPHRIES AND A. M. STUART, Runge-Kutta methods for dissipative and gradient dynamical systems, SIAM J. Numer. Anal., 31 (1994), pp. 1452-1485.
13. J. K. HALE, Asymptotic Behaviour of Dissipative Systems, AMS, New York, 1988.
14. J. K. HALE, X.-B. LIN, AND G. RAUGEL, Upper semicontinuity of attractors for approximations of semigroups and partial differential equations, Math. Comp., 50 (1988), pp. 89-123.
15. L. V. KANTOROVICH AND G. P. AKILOV, Functional Analysis in Normed Spaces, Pergamon Press, Oxford, 1964.
16. O. NEVANLINNA AND F. ODEH, Multiplier techniques for linear multistep methods, Numer. Funct. Anal. Optim., 3 (1981). pp. 377-423.
17. R. TEMAM, Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Appl. Math. Sci., 68, Springer-Verlag, Berlin, New York, 1988.