Unconditional contractivity in the maximum norm of diagonally split runge-kutta methods

SIAM Journal on Numerical Analysis

Volumn 34, Issue 2, 1997, Pages 528-543

  Bellen, A ^a   Torelli, L ^a  

^a UNIVERSITY OF TRIESTE   (Italy)

Author keywords

Diagonally split runge kutta methods; Dissipative initial value problem; Stability; Unconditional contractivity

Indexed keywords

EID: 0040133123     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994267576     Document Type: Article

References (11)

1. A. BELLEN, Z. JACKIEWICZ, AND M. ZENNARO, Contractivity of waveform relaxation Runge-Kutta methods and related limit methods for dissipative systems in the maximum norm, SIAM J. Numer. Anal., 31 (1994), pp. 499-523.
2. A. BELLEN AND M. ZENNARO, Strong contractivity properties of numerical methods for ordinary and delay differential equations, Appl. Numer. Math., 9 (1992), pp. 321-346.
3. J. C. BUTCHER, The Numerical Analysis of Ordinary Differential Equations, John Wiley, New York, 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, Order conditions for numerical methods for partitioned ordinary differential equations, Numer. Math., 36 (1981), pp. 431-445.
6. E. HAIRER, S. P. NORSETT, AND G. WANNER, Solving Ordinary Differential Equations I - Nonstiff Problems, 2nd ed., Springer-Verlag, Berlin, 1993.
7. K. J. IN 'T HOUT, A note on unconditional maximum norm contractivity of waveform relaxation Runge-Kutta methods, SIAM J. Numer. Anal., 33 (1996), pp. 1125-1134.
8. M. N. SPIJKER, Contractivity in the numerical solution of initial value problems, Numer. Math., 42 (1983), pp. 271-290.
9. M. ZENNARO, Contractivity of Runge-Kutta methods with respect to forcing terms, Appl. Numer. Math., 10 (1993), pp. 321-345.
10. E. HAIRER, private communication, NUMDIFF 7 Conference, Halle, Germany, September 1994.
11. K. J. IN 'T HOUT, private communication, Trieste, Italy, June 1994.