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STABILITIES OF (A,B,C) AND NPDIRK METHODS FOR SYSTEMS OF NEUTRAL DELAY-DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS 被引量：3

STABILITIES OF (A,B,C) AND NPDIRK METHODS FOR SYSTEMS OF NEUTRAL DELAY-DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS
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摘要 Consider the following neutral delay-differential equations with multiple delays (NMDDE)where γ> 0, L, Mj and Nj are constant complex- value d×d matrices. A sufficient condition for the asymptotic stability of NMDDE system (0.1) is given. The stability of Butcher's (A,B,C)-method for systems of NMDDE are studied. In addition, we present a parallel diagonally-implicit iteration RK (PDIRK) methods(NPDIRK) for systems of NMDDE, which is easier to be implemented than fully implicit RK methods. We also investigate the stability of a special class of NPDIRK methods by analyzing their stability behaviors of the solutions of (0.1). Consider the following neutral delay-differential equations with multiple delays (NMDDE)where γ> 0, L, Mj and Nj are constant complex- value d×d matrices. A sufficient condition for the asymptotic stability of NMDDE system (0.1) is given. The stability of Butcher's (A,B,C)-method for systems of NMDDE are studied. In addition, we present a parallel diagonally-implicit iteration RK (PDIRK) methods(NPDIRK) for systems of NMDDE, which is easier to be implemented than fully implicit RK methods. We also investigate the stability of a special class of NPDIRK methods by analyzing their stability behaviors of the solutions of (0.1).
作者 Guo-feng Zhang (Department of Mathematics, Lanzhou University, Lanzhou 730000, China)
出处 《Journal of Computational Mathematics》 SCIE CSCD 2003年第3期375-382,共8页 计算数学（英文）
关键词 Neutral delay differential equations (A B C)-method RK method Parallel diagonally-implicit iteration RK method. Neutral delay differential equations, (A,B,C)-method, RK method, Parallel diagonally-implicit iteration RK method.
分类号 O175 [理学—基础数学] O241 [理学—计算数学]
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参考文献15

  • 1A. Bellen and Z. Jackiewicz and M. Zennaro, Stability analysis of one-step methods for neutral delay-differential equations, Numer. Math., 52 (1988), 605-619.
  • 2J.C. Butcher, The numerical analysis of ordinary differential equations, 1987.
  • 3J.M. Franco and I. Gomez, Two three-parallel and three-processor SDIRK methods for stiff initialvalue problems, J. Gomput. Appl. Math., 87 (1997), 119-134.
  • 4J.M. Franco and I. Gomez, A parallel diagonally iterated RK method for convection-diffusion and stiff problems, Commun. Numer. Meth. Engng., 14 (1998), 821-837.
  • 5G.Da Hu and T. Mitsui, Stability analysis of numerical methods for systems of neutral delaydifferential equations, BIT, 35 (1995), 504-515.
  • 6G.Da Hu and G.Di Hu and S.A. Meguid, Stability of RK methods for delay differential systems with multiple delays, IMA J. Numer. Anal., 19 (1999), 349-356.
  • 7K.J. in 't Hout, A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations, BIT, 32 (1992), 634-649.
  • 8A. Iserles and G. Strang, The optimal accuracy of difference, schemes. Trans. Am. Math. Soc.,277 (1983), 779-803.
  • 9T. Koto, NP-stability of Runge-Kutta methods based on classical quadrature, BIT, 37:4 (1997),870-884.
  • 10J.X. Kuang, J.X Xiang and H.J. Tian, The asymptotic stability of one-parameter methods for neutral differential equations, BIT, 34 (1994), 400-408.

同被引文献16

  • 1CONG,Yu-hao(丛玉豪).NGP_G-STABILITY OF LINEAR MULTISTEP METHODS FOR SYSTEMS OF GENERALIZED NEUTRAL DELAY DIFFERENTIAL EQUATIONS[J].Applied Mathematics and Mechanics(English Edition),2001,22(7):827-835. 被引量：1
  • 2唐荣荣.一类非线性奇摄动方程的激波问题(英文)[J].数学进展,2005,34(2):233-240. 被引量：16
  • 3冯茂春.二次方程Robin问题奇摄动群的估计[J].应用数学,2007,20(3):467-472. 被引量：5
  • 4Kuang Y.Delay Differential Equations with Application in Population Dynamics[]..1993
  • 5Fridman E.New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems[].Systems and Control Letters.2001
  • 6Brayton RK,Willoughby RA.On the numerical integration of a symmetric system of difference-differential equations of neutral type[].Journal of Mathematical.1967
  • 7DATKO R.Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks[].SI AMJournal on Control and Optimization.1988
  • 8Logemann H,Rebarber R,Weiss G.Conditions for Robustness and Nonrobustness of the Stability of Feedback Systems with Respect to Small Delays in the Feedback Loop[].SI AM Journal on Control and Optimization.1996
  • 9Chen Xianfeng,Yu Pei,Han Maoan,Zhang Weijiang.Canard solutions of two-dimensional singularly perturbed systems[].Chaos Solitons Fractals.2005
  • 10Hadd S.Singular functional differential equations of neutral type in Banachspaces[].Journal of Functional Analysis.2008

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Journal of Computational Mathematics
2003年 第3期

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