On error growth functions of Runge-Kutta methods

Applied Numerical Mathematics

Volumn 22, Issue 1-3 SPEC. ISS., 1996, Pages 205-216

  Hairer, E ^a   Zennaro, M ^b  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b UNIVERSITY OF TRIESTE   (Italy)

Author keywords

Asymptotic stability; B stability; Error growth functions; Runge Kutta methods; Stiff differential equations; Superexponential functions

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; ESTIMATION; FUNCTIONS;

ERROR GROWTH FUNCTIONS; RUNGE KUTTA METHODS; STIFF DIFFERENTIAL EQUATIONS;

NUMERICAL METHODS;

EID: 0030287583     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0168-9274(96)00032-3     Document Type: Article

References (9)

1. K. Burrage and J.C. Butcher, Stability criteria for implicit Runge-Kutta methods, SIAM J. Numer. Anal. 16 (1979) 46-57.
2. K. Burrage and J.C. Butcher, Non-linear stability of a general class of differential equation methods, BIT 20 (1980) 185-203.
3. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations (Wiley, London, 1987).
4. K. Dekker and J.G. Verwer, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations (North-Holland, Amsterdam, 1984).
5. E. Hairer, S.P. Nørsett and G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems (Springer, New York, 2nd ed., 1993).
6. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential Algebraic Problems (Springer, New York, 2nd ed., 1996).
7. E. Hairer and G. Wanner, On a generalization of a theorem of von Neumann, Z. Angew. Math. Mech., to appear.
8. W.H. Hundsdorfer and M.N. Spijker, A note on B-stability of Runge-Kutta methods, Numer. Math. 36 (1981) 319-331.
9. A.M. Stuart and A.R. Humphries, Model problems in numerical stability theory for initial value problems, SIAM Rev. 36 (1994) 226-257.