Linear multistep methods as irreducible general linear methods

BIT Numerical Mathematics

Volumn 46, Issue 1, 2006, Pages 5-19

  Butcher, J C ^a   Hill, A T ^b  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b University of Bath   (United Kingdom)

Author keywords

G stability; General linear methods; Linear multistep methods

Indexed keywords

EID: 33645038609     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-006-0046-3     Document Type: Article

References (15)

1. A. Albert, Conditions for positive and non-negative definiteness in terms of pseudo-inverses, SIAM J. Appl. Math., 17 (1969), pp. 434-440.
2. C. Baiocchi and M. Crouzeix, On the equivalence of A-stability and G-stability, Appl. Numer. Math., 5 (1989), pp. 19-22.
3. K. Burrage and J. C. Butcher, Non-linear stability of a general class of differential equation methods, BIT, 20 (1980), pp. 185-204.
4. J. C. Butcher, The equivalence of algebraic stability and AN-stability, BIT, 27 (1987), pp. 510-534.
5. G. Dalilquist, Error analysis for a class of methods for stiff nonlinear initial value problems, Proceedings of the 1975 Dundee Conference in Numerical Analysis, Springer Lecture Notes in Mathematics, 506 (1976), pp. 60-75.
6. G. Dahlquist, G-stability is equivalent to A-stability, BIT, 18 (1978), pp. 384-401.
7. G. Dahlquist, On one-leg multistep methods, SIAM J. Numer. Anal., 20 (1983), pp. 11301138.
8. G. Dahlquist and G. Söderlind, Some problems related to stiff nonlinear differential systems, in Computing Methods in Applied Sciences and Engineering, R. Glowinski and J. L. Lions (eds.), North Holland, INRIA, 1982.
9. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Springer, Berlin, 1991.
10. E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration, Springer, Berlin, 2002.
11. W. Hundsdorfer and B. I. Steininger, Convergence of linear multistep and one-leg methods for stiff nonlinear initial value problems, BIT, 31 (1991), pp. 124-144.
12. W. Hundsdorfer, On the error of general linear methods for stiff dissipative differential equations, IMA J. Numer. Anal., 14 (1994), pp. 363-379.
13. O. Nevanlinna, On the numerical integration of nonlinear initial value problems, BIT, 17 (1977), pp. 58-71.
14. R. D. Skeel, Equivalent forms of multistep formulas, Math. Comput. 33 (1979), pp. 1229-1250.
15. M. Vidyasagar, Nonlinear Systems Analysis, 2nd edn., Prentice Hall, Englewood Cliffs, NJ, 2002.