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非线性MDDEs一般线性方法的稳定性分析

The Stability of General Linear Methods for Nonlinear Multi-Delay Differential Equations
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摘要 本文给出了非线性MDDEs(多延迟微分方程)的一般线性方法GR(p,q)-稳定的一个充分条件,并将[1]的部分工作推广到了多延迟的情形,获得了较好的结论。 In this paper, we gave a sufficient condition of GR(p.q)-stability for nonlinear Multi-Delays Differential Equations and then, we discuss the case of many delays which depends on the part work in the thesis of Huang and gain some similar results.
出处 《长春师范学院学报(自然科学版)》 2004年第3期6-8,共3页 Journal of Changchun Teachers College
基金 湖南省教育厅资助科研项目(02C568)
关键词 非线性MDDEs 一般线性方法 稳定性分析 GR(p q)-稳定 (k p q)-代数稳定 初值问题 multi-delays differential equations general linear methods GR(p,q)-stability (k,p,q) -stability
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参考文献6

  • 1[1]Huang Cheng-ming, Numerical analysis of nonlinear delay differential equations [D]. Ph. D. Thesis. Graduate School of china Academy of Engineering Physics. 1999.
  • 2张诚坚.非线性MDDEs系统的隐式Euler法的稳定性[J].湖南大学学报(自然科学版),1998,25(1):1-4. 被引量:12
  • 3[5]G. D. Hu and T. Mitsui, Stability analysis of numerical methods for systems of neutral delay differential equations[M]. B1T, 35(1995),504~515.
  • 4[6]Zhang Chengjian, Liao Xiaoxin, Asymptotic behavior of multi step Runge-Kutta methods for systems of delay differential equations[J]. Acta Mathematice Applicatae Sinica Vol,17. No. 2. 2001. 240~260.
  • 5[7]TIAN H. J. KUANG J. X. The stability of the θ-methods in the numerical solution of delay differential equations with several delay terms [J]. J (comput. appl. math, 1995,58 : 171 ~ 181 ).
  • 6[8]K. J. in,t Hout and M. N. Spijker,The θ-methods in the numerical solution of delay differential equations[M]. Proceedings of the International Seminar NUMDIFF-5,Teubner,Leipzig,1989.

二级参考文献2

  • 1Tian H J,SIAM J Numer Anal,1996年,33卷,3期,883页
  • 2Liu M Z,IMA J Numer Anal,1990年,10期,31页

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