Regular Runge-Kutta pairs

Applied Numerical Mathematics

Volumn 25, Issue 2-3, 1997, Pages 229-241

  Higham, Desmond J ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Error control; Spurious fixed point; Variable time stepping

Indexed keywords

ERROR ANALYSIS; FITS AND TOLERANCES; NUMERICAL ANALYSIS; RECURSIVE FUNCTIONS; STABILITY;

RUNGE-KUTTA METHODS;

TIME DOMAIN ANALYSIS;

EID: 0031276341     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(97)00062-7     Document Type: Article

References (8)

1. M.A. Aves, D.F. Griffiths and D.J. Higham, Does error control suppress spuriosity? SIAM J. Numer. Anal. 34 (1997) 756-778.
2. E. Fehlberg, Klassiche Runge-Kutta-Formeln vierter und niedriger Ordnung mit Schrittweiten-Kontrolle und ihre Andwendung auf Wärmeleitungsprobleme, Computing 6 (1970) 61-71.
3. E. Hairer, A. Iserles and J.M. Sanz-Serna, Equilibria of Runge-Kutta methods, Numer. Math. 58 (1990) 243-254.
4. G. Hall, Equilibrium states of Runge-Kutta schemes, ACM Trans. Math. Software 11 (1985) 289-301.
5. A.R. Humphries, Spurious solutions of numerical methods for initial value problems, IMA J. Numer. Anal. 13 (1993) 263-290.
6. A. Iserles, Stability and dynamics of numerical methods for nonlinear ordinary differential equations, IMA J. Numer. Anal. 10 (1990) 1-30.
7. Z. Jackiewicz, R. Vermiglio and M. Zennaro, Regularity properties of Runge-Kutta methods for ordinary differential equations, Appl. Numer. Math. 22 (1996) 251-262.
8. Z. Jackiewicz, R. Vermiglio and M. Zennaro, Regularity properties of Runge-Kutta methods for delay differential equations, Appl. Numer. Math. 24 (1997) 263-278.