NGP<sub>G</sub>-Stability of Linear Multistep Methods for Systems of Generalized Neutral Delay Differential Equations

CONG Yu-hao

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Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(7): 735-742

CONG Yu-hao. NGPG-Stability of Linear Multistep Methods for Systems of Generalized Neutral Delay Differential Equations[J]. Applied Mathematics and Mechanics, 2001, 22(7): 735-742.

Citation:

CONG Yu-hao. NGP_G-Stability of Linear Multistep Methods for Systems of Generalized Neutral Delay Differential Equations[J]. Applied Mathematics and Mechanics, 2001, 22(7): 735-742.

CONG Yu-hao. NGPG-Stability of Linear Multistep Methods for Systems of Generalized Neutral Delay Differential Equations[J]. Applied Mathematics and Mechanics, 2001, 22(7): 735-742.

Citation:

CONG Yu-hao. NGP_G-Stability of Linear Multistep Methods for Systems of Generalized Neutral Delay Differential Equations[J]. Applied Mathematics and Mechanics, 2001, 22(7): 735-742.

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NGP_G-Stability of Linear Multistep Methods for Systems of Generalized Neutral Delay Differential Equations

CONG Yu-hao

Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

Received Date: 2000-03-03
Rev Recd Date: 2001-03-30
Publish Date: 2001-07-15

Abstract

Abstract

The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations. After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP_G-stable if and only if it is A-stable.
- generalized neutral delay differential system,
- asymptotic stability,
- linear multistep methods,
- NGP_G-stability

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References(20)

References

[1]	Brayton R K,Willoughby R A.On the numerical intergration of a symmetric system of a difference-differential equations[J].J Math Anal Appl,1967,18(1):182-189.
[2]	Jackiewicz Z.One-step methods of any order for neutral functional differential equations[J].SIAM J Numer Anal,1984,21(3):486-511.
[3]	Bellen A,Jackiewicz Z,Zennaro M.Stability analysis of one-step methods for neutral delay-differential equations[J].Numer Math,1988,52(3):605-619.
[4]	KUANG Jiao-xun,XIANG Jia-xiang,TIAN Hong-jun.The asymptotic stability of one-parameter methods for neutral differential equations[J].BIT,1994,34(3):400-408.
[5]	HU Guang-da,Mitsui T.Stability of numerical methods for systems of neutral delay differential equations[J].BIT,1995,35(4):504-515.
[6]	HU Guang-di,HU Guang-da.Some simple criteria for stability of neutral delay-differential system[J].Appl Math Compu,1996,80(2-3):257-271.
[7]	QIU Lin,YANG Biao,KUANG Jiao-xun.The NGP-stability of Runge-Kutta methods for systems of neutral delay differential equations[J].Numer Math,1999,81(3):451-459.
[8]	ZHANG Cheng-jiang,ZHOU Shu-zi.Stability analysis of LMMs for systems neutral multidelay-differential equations[J].J Computers and Mathematics With Application,1999,38(1):113-117.
[9]	Koto T.A stability property of A-stable natural Runge-Kutta methods for systems of delay differential equations[J].BIT,1994,34(2):262-267.
[10]	In't Hout K J.Stability analysis of Runge-Kutta methods for systems of delay differential equations[J].IMA J Numer Anal.1997,17(1):17-27.
[11]	Desoer A,Vidyasagas M.Feedback Systems:Input-Output Properties[M].New York:Academic Press,1975.
[12]	Lancaster P,Tismenetsky M.The Theory of Matrices[M].Orland,Florida:Academic press,1985.
[13]	Strang G.Trigonometric polynomials and difference methods of maximum accuracy[J].J Math Phys,1962,41(1):147-154.
[14]	Iserles A,Strang G.The optimal accuracy of difference schemes[J].Trans Amer Math Soc,1983,277(2):299-303.
[15]	Barwell V K.Special stability problem for functional differential equations[J].BIT,1975,15(2):130-135.
[16]	LIU Ming-zhu,Spijker M N.The stability of θ-methods in the numerical solution[J].IMA Numer Anal,1990,10(1):31-48.
[17]	In't Hout K J.A new interpolation procedure for adapting Runge-Kutta methods for delay differential equations[J].BIT,1992,32(4):634-649.
[18]	YANG Biao,QIU Lin,T Mitsui.GPG-stability of Runge-Kutta methods for generalized delay differential systems[J].J Computers and Mathematics With Application,1999,37(1):89-97.
[19]	HU Guang-da,HU Guang-di.Stability of neutral delay-differential systems:boundary criteria[J].Appl Math Compu[J].1997,87(2-3):247-259.
[20]	ZHANG Cheng-jian,ZHOU Shu-zi.The asymptotic stability of theoretical and numerical solutions for systems of neutral multidelay-differential equations[J].Science in China.1998,41(11):1153-1157.