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Section B

Stability of two-step Runge–Kutta methods for neutral delay differential-algebraic equations

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Pages 375-383 | Received 28 Oct 2008, Accepted 25 Oct 2009, Published online: 15 Dec 2010

References

  • Brenan , K. E. , Campbell , S. L. and Petzold , L. R. 1995 . Numerical Solution of Initial-Value Problem in Differential-Algebraic Equations , 2 , Philadelphia, PA : SIAM .
  • Cullum , J. , Ruehli , A. and Zhang , T. 2000 . A method for reduced-order modeling and simulation of large interconnect circuits and its application to PEEC models with retardation . IEEE Trans. Circuits Syst. Analog Digit. Signal Process , 47 : 261 – 273 .
  • Hairer , E. , Norsett , S. P. and Wanner , G. 1992 . Solving Ordinary Differential-algebraic Equations II: Stiff and Differential-Algebraic Problems , New York : Springer .
  • Jackiewicz , Z. , Renaut , R. and Feldstent , A. 1991 . Two-step Runge–Kutta methods . SIAM J. Numer. Anal. , 28 : 1165 – 1182 .
  • Liu , M. Z. and Spijker , M. N. 1990 . The stability of the θ-methods in the numerical solution of delay differential equations . IMA J. Numer. Anal. , 10 ( 1 ) : 31 – 48 .
  • Petzold , L. R. 1995 . “ Numerical Solutions of Differential-Algebraic Equations ” . In Theory and Numerics of Ordinary and Partial Differential Equations , Oxford : Oxford University Press .
  • Zennaro , M. 1995 . “ Delay differential equations: Theory and numerics ” . In Theory and Numerics of Ordinary and Partial Differential Equations , Edited by: Ainsworth , M. , Levesley , J. , Light , W. A. and Marletta , M. Oxford : Oxford University Press .
  • Zhao , J. J. , Xu , Y. , Dong , S. Y. and Liu , M. Z. 2005 . Stability of the Ronsenbrock methods for the neutral delay differential-algebraic equations . Appl. Math. Comput. , 168 : 1128 – 1144 .
  • Zhu , W. and Petzold , L. R. 1997 . Asymptotic stability of linear delay differential-algebraic equations and numerical methods . Appl. Numer. Math. , 24 : 247 – 264 .

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