Methods for linear systems of circuit delay differential equations of neutral type

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 46, Issue 1, 1999, Pages 212-216

  Bellen, Alfredo ^a   Guglielmi, Nicola ^a   Ruehli, Albert E ^a  

^a UNIVERSITY OF TRIESTE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; ELECTRIC DELAY LINES; EQUIVALENT CIRCUITS; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; VLSI CIRCUITS;

DELAY DIFFERENTIAL EQUATIONS (DDE);

LINEAR NETWORK ANALYSIS;

EID: 0032778117     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.739268     Document Type: Article

References (16)

1. C.T.H. Baker, C.A.H. Paul, and D.R. Wille, "Issues in the numerical solution of evolutionary delay differential equations," Adv. Comp. Math, vol. 3, pp. 171-196, 1995.
2. R.K. Brayton, "Small signal stability criterion for networks containing lossless transmission lines," IBM J. Res. Develop., vol. 12, pp. 431-140, 1968.
3. A.E. Ruehli, "Equivalent circuit models for three dimensional multiconductor systems," IEEE Trans. Microwave Theory Tech., vol. 22, pp. 216-22, Mar. 1974.
4. A.E. Ruehli, U. Miekkala, A. Bellen, and H. Heeb, "Stable time domain solutions for EMC problems using PEEC circuit models," in Proc. of Inter. Symp. on Elmag. Comp., Chicago, IL, Aug. 1994, pp. 371-376.
5. L.M. Li, "Stability of linear neutral delay-differential systems," Bull. Australian Math. Soc., vol. 38, pp. 339-344, 1988.
6. G.-D. Hu and T. Mitsui, "Stability analysis of numerical methods for systems of neutral delay-differential equations," BIT, vol. 35, pp. 504-515, 1995.
7. L. Torelli, "A sufficient condition for GPN-stability for delay diff. eq.," Numer. Math., vol. 59, pp. 311-320, 1991.
8. A. Bellen and M. Zennaro, "Strong contractivity properties of numerical methods for ordinary and delay differential equations," Appl. Numer. Math., vol. 9, pp. 321-346, 1992.
9. M. Slemrod and E.F. Infante, "Asymptotic stability criteria for linear systems of difference-differential equations of neutral type and their discrete analogues," J. Math. Appl., vol. 38, pp. 399-115, 1972.
10. A. Bellen, N. Guglielmi, and A. Ruehli, "On a class of stable methods for linear systems of delay differential euqaions of neutral type," Tech. Rep., IBM Watson Res. Rep., Yorktown Heights, NY, RC 21253, May 1998.
11. M. Zennaro, "Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations," Num. Math., vol. 77, no. 4, pp. 549-563, 1997.
12. T. Mori, N. Fukuma, and M. Kuwahara, "Simple stability criteria for single and composite linear systems with time delays," Int.J. Contr., vol. 34, no. 6, pp. 1175-1184, 1981.
13. K.J. in 't Hout, "A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations," BIT, vol 32, pp. 634-649, 1992.
14. A. Bellen, "One-step collocation for delay differential equations," J. Comput. Appl. Math., vol. 10, pp. 275-283, 1984.
15. A. Bellen and M. Zennaro, Numerical Methods for Delay Differential Equations, in preparation.
16. W. Pinello, A.C. Cangellaris, and A. Ruehli, "Hybrid electromagnetic modeling of noise interactions in packaged electronics based on the partial element equivalent circuit formulation," IEEE Trans. Microwave Theory Tech., vol. 45, pp. 1889-1896, Oct. 1997.