Iterated Runge-Kutta methods of implicit differential-algebraic equations

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

Volumn 13, Issue 5, 2006, Pages 555-567

  Sun, Wei ^a,b   Fan, Xiao Guang ^a   Wang, Yu Ying ^b  

^a AIR FORCE ENGINEERING UNIVERSITY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Converge; Implicit differential algebraic equations; Parallelism; Runge kutta methods; Waveform relaxation

Indexed keywords

EID: 33750395823     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. E. Hairer, G. Wanner, Solving ordinary differential equations, II stiff and differential-algebraic problems, Springer-Verlag Press, Berlin, 1991.
2. E. Hairer, Chr. Lubich, and M. Roche, The numerical solution of differential-algebraic systems by Runge-Kutta methods, LNM1409, Springer Press, Berlin, 1989.
3. P. J. van der Houwen and B. P. Sommeijer, Iterated Runge-Kutta methods on parallel computers, SIAM J. Sci. Stat. Comput. 12, (1991) 1000-1028.
4. P. J. van der Houwen and W. A. van der Veen, : Waveform relaxation methods for implicit differential equations, Advances in Comput. Math. 12, (1997) 183-197.
5. E. Lelarasmee, A. E. Ruehli, and A. L. Sangiovanni-Vincentellli, The waveform relaxation method for time-domain analysis of large scale integrated circuits, IEEE Trans. CAD IC Syst. 1, (1982) 131-145.
6. Y. L. Jiang, Richard M. M. Chen, and O. Wing, Convergence analysis of Waveform Relaxation for nonlinear differential-algebraic equations of index one, IEEE Trans. on Circuits and Systems: Fundamental Theory and Applications, 47(11), (2000) 1639-1645.
7. J. C. Butcher, A transformed implicit Runge-Kutta methods, J. Assoc. Comput. Math. 26, (1979) 731-738.
8. K. Burrage, Parallel and sequential methods for ordinary differential equations, Clarendon Press, Oxford, 1995.
9. J. C. Butcher, On the implementation of implicit Runge-Kutta methods, BIT 16, (1976) 237-240.
10. A. Bellen, Parallelism across the steps for difference and differential equations, in: A. Bellen, C. W. Gear, & E. Russo, eds., Numerical methods for ordinary differential equations, 23-35, LNM1386 Springer, Berlin, 1987.
11. A. Bellen, Z. Jackiewicz, and M. Zennaro, Time-point relaxation Runge-Kutta methods for ordinary differential equations, J. Comput. Appl. Math. 45, (1993) 121-137.
12. P. J. van der Houwen and J. B. de Swart, Triangularly implicit iteration methods for ODE-IVP solvers, SIAM J. Sci. Comput. 18, (1997) 41-55.
13. P. J. van der Houwen and W. A. van der Veen, Solving implicit differential equations on paeallel computers, CWI Report NM-R9526, 1995.