NP-stability of Runge-Kutta methods based on classical quadrature

BIT Numerical Mathematics

Volumn 37, Issue 4, 1997, Pages 870-884

  Koto, T ^a  

^a UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

Author keywords

Implicit Runge Kutta methods; Neutral delay differential equations; NP stability

Indexed keywords

EID: 0006554105     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510357     Document Type: Article

References (15)

1. V. K. Barwell, Special stability problems for functional differential equations, BIT, 15 (1975), pp. 130-135.
2. A. Bellen, Z. Jackiewicz, and M. Zennaro, Stability analysis of one-step methods for neutral delay-differential equations, Numer. Math., 52 (1988), pp. 605-619.
3. J. C. Butcher, On A-stable implicit Runge-Kutta methods, BIT, 17 (1977), pp. 375-378.
4. J. C. Butcher, The Numerical Analysis of Ordinary Differential Equations. Runge-Kutta and General Linear Methods, John Wiley & Sons, Chichester, 1987.
5. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Springer-Verlag, Berlin, Heidelberg, New York, 1991.
6. G.-D. Hu and T. Mitsui, Stability analysis of numerical methods for sysytems of neutral delay-differential equations, BIT, 35 (1995), pp. 504-515.
7. K. J. in't Hout and M. N. Spijker, Stability analysis of numerical methods for delay differential equations, Numer. Math., 59 (1991), pp. 807-814.
8. T. Koto, A stability property of A-stable collocation-based Runge-Kutta methods for neutral delay differential equations, BIT, 36 (1996), pp. 855-859.
9. S. P. Nørsett and G. Wanner, Perturbed collocation and Runge-Kutta methods, Numer. Math., 38 (1981), pp. 193-208.
10. L. Torelli, A sufficient condition for GPN-stability for delay differential equations, Numer. Math., 59 (1991), pp. 311-320.
11. D. S. Watanabe and M. G. Roth, The Stability of difference formulas for delay differential equations, SIAM J. Numer. Anal., 22 (1985), pp. 132-145.
12. M. Zennaro, Natural continuous extensions of Runge-Kutta methods, Math. Comput., 46 (1986), pp. 119-133.
13. M. Zennaro, P-stability properties of Runge-Kutta methods for delay differential equations, Numer. Math., 49 (1986), pp. 305-318.
14. M. Zennaro, Natural Runge-Kutta and projection methods, Numer. Math., 53 (1988), pp. 423-438.
15. M. Zennaro, Delay differential equations: Theory and numerics, in M. Ainsworth, J. Levesley, W. A. Light and M. Marietta (ed.), Theory and Numerics of Ordinary and Partial Differential Equations, pp. 291-333, Oxford University Press, Oxford, 1995.