Waveform relaxation as a dynamical system

Mathematics of Computation

Volumn 66, Issue 219, 1997, Pages 1101-1117

  Bjørhus, Morten ^a,b   Stuart, Andrew M ^c  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b NORWEGIAN DEFENCE RESEARCH ESTABLISHMENT FFI   (Norway)

^c Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031534567     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-97-00847-8     Document Type: Article

References (11)

1. Alfredo Bellen and Marino Zennaro, The use of Runge-Kutta formulae in waveform relaxation methods, Appl. Numer. Math. 11 (1993), 95 -114. MR 94c:65090
2. Morten Bjørhus, A note on the convergence of discretized dynamic iteration, BIT 35 (1995), 291-296.
3. J. K. Hale, Ordinary differential equations, Wiley, Chichester, 1969. MR 54:7918
4. _, Asymptotic behaviour of dissipative systems, Mathematical surveys and Monographs, no. 25, AMS, Providence, Rhode Island, 1988. MR 89g:58059
5. M. Hirsch, C. Pugh, and M. Shub, Invariant manifolds, Springer-Verlag, New York, 1977. MR 58:18595
6. Arieh Iserles, Stability and dynamics of numerical methods for nonlinear ordinary differential equations, IMA J. Num. Anal. 10 (1990), 1-30. MR 91e:65105
7. Ekachai Lelarasmee, Albert E. Ruehli, and Alberto L. Sangiovanni-Vincentelli, The waveform relaxation method for time-domain analysis of large scale integrated circuits, IEEE Trans. on CAD of IC and Syst. 1 (1982), 131-145.
8. Ulla Miekkala and Olavi Nevanlinna, Convergence of dynamic iteration methods for initial value problems, SIAM J. Sci. Stat. Comput. 8 (1987), 459-482. MR 89f:65076
9. Olavi Nevanlinna, Remarks on Picard-Lindelöf iteration, BIT 29 (1989), 328-346, 535-562. MR 91b:65088
10. Andrew M. Stuart, Perturbation theory for infinite dimensional dynamical systems, Advances in Numerical Analysis (M. Ainsworth. J. Levesley, W.A. Light, and M. Marletta, eds.), Oxford University Press, 1995. CMP 96:05
11. Andrew M. Stuart and A. R. Humphries, Dynamical systems and numerical analysis, Cambridge University Press, Cambridge, 1996. CMP 96:16