求解广义中立型系统的线性多步方法的NGP<sub>G</sub>-稳定性

丛玉豪

求解广义中立型系统的线性多步方法的NGP_G-稳定性

丛玉豪

上海师范大学数学科学学院, 上海 200234

基金项目: 上海市教委青年科学基金资助项目(99QA80);上海市科学技术发展基金资助项目(00JC14057)

详细信息

作者简介:
丛玉豪(1965- ),男,山东人,博士,副教授.

中图分类号: O241.81
计量
- 文章访问数: 2635
- HTML全文浏览量: 186
- PDF下载量: 618
- 被引次数: 0
出版历程
- 收稿日期: 2000-03-03
- 修回日期: 2001-03-30
- 刊出日期: 2001-07-15

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

摘要

摘要: 建立了广义中立型延迟系统理论解渐近稳定的充分条件,分析了用线性多步方法求解广义中立型延迟系统数值解的稳定性,在一定的Lagrange插值条件下,证明了数值求解广义中立型系统的线性多步方法NGP_G-稳定的充分必要条件是线性多步方法是A-稳定的.
- 广义中立型系统 /
- 渐近稳定性 /
- 线性多步方法 /
- NGPG-稳定性
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

HTML全文

参考文献(20)

[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.