留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

求解时滞微分方程组的Rosenbrock方法的GP-稳定性

丛玉豪 才佳宁 项家祥

丛玉豪, 才佳宁, 项家祥. 求解时滞微分方程组的Rosenbrock方法的GP-稳定性[J]. 应用数学和力学, 2004, 25(12): 1285-1291.
引用本文: 丛玉豪, 才佳宁, 项家祥. 求解时滞微分方程组的Rosenbrock方法的GP-稳定性[J]. 应用数学和力学, 2004, 25(12): 1285-1291.
CONG Yu-hao, CAI Jia-ning, XIANG Jia-xiang. GP-Stability of Rosenbrock Methods for System of Delay Differential Equation[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1285-1291.
Citation: CONG Yu-hao, CAI Jia-ning, XIANG Jia-xiang. GP-Stability of Rosenbrock Methods for System of Delay Differential Equation[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1285-1291.

求解时滞微分方程组的Rosenbrock方法的GP-稳定性

基金项目: 国家自然科学基金资助项目(10171067)
详细信息
    作者简介:

    丛玉豪(1965- ),男,山东人,教授,博士(联系人.Tel/Fax:+86-21-64321049;E-mail:yhcong@shnu.edu.cn).

  • 中图分类号: O241.8

GP-Stability of Rosenbrock Methods for System of Delay Differential Equation

  • 摘要: 讨论了求解延时微分方程组的Rosenbrock方法的数值稳定性,分析了求解线性试验方程组的Rosenbrock方法的稳定性态,并证明了数值求解延时微分方程组的Rosenbrock方法是GP-稳定的充分必要条件是Rosenbrock方法是A-稳定的.
  • [1] Bellen A, Jackiewicz Z, Zennaro M.Stability analysis of one-step methods for neutral delay-differential equations[J].Numerische Mathematik,1988,52(3):605—619. doi: 10.1007/BF01395814
    [2] LIU Ming-zhu,Spijker M N.The stability of θ-methods in the numerical solution[J].IMA Journal of Numerical Analysis, 1990,10(1):31—48. doi: 10.1093/imanum/10.1.31
    [3] in't Hout K J.The stability of θ-methods for systems of delay differential equations[J].Annals of Numerical Mathematics,1994,1(3):323—334.
    [4] 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. doi: 10.1007/BF01955873
    [5] HU Guang-da,Mitsui T.Stability of numerical methods for systems of nautral delay differential equations[J].BIT,1995,35(4):504—515. doi: 10.1007/BF01739823
    [6] Hairer E,Nrsett S P,Wanner G.Solving Ordinary Differential Equations[M].New York:Springer-Verlag,2000,103—117.
    [7] 曹学年,刘德贵,李寿佛.求解延迟微分方程的Rosenbrock方法的渐近稳定性[J].系统仿真学报, 2002,14(3):290—292.
    [8] Lambert J D.Computational Methods in Ordinary Differentail Equations[M].New York:John-Willy,1990.
    [9] KUANG Jiao-xun,TIAN Hong-jiong.The asymptotic behaviour of theoretical and numerical solutions for nonlinear differential systems with several delay terms[J].Journal of Shanghai Teachers University(Natural Sciences),1995,24(1):1—7.
    [10] in't Hout K J.A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations[J].BIT,1992,32(4):634—649. doi: 10.1007/BF01994847
    [11] 匡蛟勋.块θ方法的PL-稳定性[J].计算数学,1997,15(2):135—140.
    [12] YANG Biao,QIU Lin,KUANG Jiao-xun.The GPL-stability of Runge-Kutta methods for delay differential systems[J].J Comput Math,2000,18(1):75—82.
    [13] Huang C M, Li S F,Fu H Y,et al.Stability and error analysis of one-leg methods for nonlinear delay differential equations[J].Journal of Computational and Applied Mathematics,1999,103(2):263—279. doi: 10.1016/S0377-0427(98)00262-3
    [14] CHEN Li-rong, LIU De-gui.Combined RK-Rosenbrock methods and their stability[J].Mathematica Numerica Sinica,2000,22(3):319—332.
    [15] LI Shou-fu.Nonlinear stability of general linear methods[J].Journal of Computational Mathematics,1991,9(2):97—104.
    [16] Robert Piché.An L-stable Rosenbrock method for step-by-step time integration in structual dynamics[J].Computer Methods in Applied Mechanics and Engineering,1995,126(3/4):343—354. doi: 10.1016/0045-7825(95)00823-J
    [17] SUN Geng.A class of single step methods with a large interval of absolute stability[J].J Comput Math,1991,9(2):185—193.
    [18] Barwell V K.Special stability problems for functional differential equations[J].BIT,1975,15(2):130—135. doi: 10.1007/BF01932685
    [19] ZHANG Cheng-jian, ZHOU Shu-zi.Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations[J].Journal of Computational and Applied Mathematics,1997,85(2):225—237. doi: 10.1016/S0377-0427(97)00118-0
  • 加载中
计量
  • 文章访问数:  2252
  • HTML全文浏览量:  107
  • PDF下载量:  947
  • 被引次数: 0
出版历程
  • 收稿日期:  2003-04-22
  • 修回日期:  2004-07-06
  • 刊出日期:  2004-12-15

目录

    /

    返回文章
    返回