메뉴 건너뛰기




Volumn 21, Issue 6, 2003, Pages 715-726

Dissipativity and exponential stability of θ-methods for singularly perturbed delay differential equations with a bounded lag

Author keywords

methods; Dissipativity; Exponential stability; Singular perturbation

Indexed keywords

DIFFERENTIAL EQUATIONS; NUMERICAL METHODS; STABILITY;

EID: 1542331706     PISSN: 02549409     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (9)

References (23)
  • 1
    • 0019703221 scopus 로고
    • Fixed discretization methods for delay differential equations
    • K. Allen and S. McKee, Fixed discretization methods for delay differential equations, Comp. and Math. with Appl., 7(1981), 413-423.
    • (1981) Comp. and Math. with Appl. , vol.7 , pp. 413-423
    • Allen, K.1    McKee, S.2
  • 2
    • 0006716535 scopus 로고    scopus 로고
    • Generalized Halanay inequalities for Volterra functional differential equations and the discrete versions
    • Arlington
    • C. T. H. Baker and A. Tang, Generalized Halanay inequalities for Volterra functional differential equations and the discrete versions, Volterra Centennial Meeting, Arlington, June, 1996.
    • (1996) Volterra Centennial Meeting
    • Baker, C.T.H.1    Tang, A.2
  • 3
    • 0031208947 scopus 로고    scopus 로고
    • Contractivity of continuous Runge-Kutta methods for delay differential equations
    • A. Bellen, Contractivity of continuous Runge-Kutta methods for delay differential equations, Appl. Numer. Math. 24 (1997), 219-231.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 219-231
    • Bellen, A.1
  • 5
    • 0002087132 scopus 로고
    • The condition of regular degeneration for singularly perturbed linear differential-difference equations
    • K. L. Cooke, The condition of regular degeneration for singularly perturbed linear differential-difference equations, J. Diff. Eqns., 1(1965), 39-94.
    • (1965) J. Diff. Eqns. , vol.1 , pp. 39-94
    • Cooke, K.L.1
  • 10
    • 0001599522 scopus 로고
    • Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
    • E. Hairer, C. Lubich and M. Roche, Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations, BIT, 28 (1988), 678-700.
    • (1988) BIT , vol.28 , pp. 678-700
    • Hairer, E.1    Lubich, C.2    Roche, M.3
  • 13
    • 0018508810 scopus 로고
    • Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system
    • K. Ikeda, Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system, Opt. Comm., 30 (1979), 257.
    • (1979) Opt. Comm. , vol.30 , pp. 257
    • Ikeda, K.1
  • 14
    • 0000714267 scopus 로고
    • The stability of the θ-methods in the numerical solution of delay differential equations
    • M.Z. Liu and M.N. Spijker, The stability of the θ-methods in the numerical solution of delay differential equations, IMA J. Numer. Anal. 10 (1990), 31-48.
    • (1990) IMA J. Numer. Anal. , vol.10 , pp. 31-48
    • Liu, M.Z.1    Spijker, M.N.2
  • 15
    • 0023718682 scopus 로고
    • Complex oscillations in the human pupil light reflex with mixed and delayed feedback
    • A. Longtin, and J. Milton, Complex oscillations in the human pupil light reflex with mixed and delayed feedback, Math. Biosciences, 90 (1988), 183-199.
    • (1988) Math. Biosciences , vol.90 , pp. 183-199
    • Longtin, A.1    Milton, J.2
  • 16
    • 0017714604 scopus 로고
    • Oscillation and chaos in physiological control systems
    • M. C. Mackey, and L. Glass, Oscillation and chaos in physiological control systems, Science, 197(1977), 287-289.
    • (1977) Science , vol.197 , pp. 287-289
    • Mackey, M.C.1    Glass, L.2
  • 18
    • 0005715126 scopus 로고    scopus 로고
    • Numerical treatment of singularly perturbed delay differential equations
    • Ph.D. thesis, University of Manchester
    • H. Tian, Numerical Treatment of Singularly Perturbed Delay Differential Equations, Ph.D. thesis, University of Manchester, 2000.
    • (2000)
    • Tian, H.1
  • 19
    • 0005717397 scopus 로고    scopus 로고
    • The stability analysis of θ-methods for delay differential equations
    • H. Tian and J. Kuang, The stability analysis of θ-methods for delay differential equations, J. Comp. Math., 14 (1996), 203-212.
    • (1996) J. Comp. Math. , vol.14 , pp. 203-212
    • Tian, H.1    Kuang, J.2
  • 20
    • 25944445518 scopus 로고    scopus 로고
    • Numerical and analytic dissipativity of delay differential equations
    • Submitted
    • H. Tian, Numerical and analytic dissipativity of delay differential equations. Submitted, 2001.
    • (2001)
    • Tian, H.1
  • 21
    • 0005715127 scopus 로고
    • A sufficient condition for GPN-stability for delay differential equations
    • L. Torelli, A sufficient condition for GPN-stability for delay differential equations, Numer. Math., 25(1991), 311-320.
    • (1991) Numer. Math. , vol.25 , pp. 311-320
    • Torelli, L.1
  • 22
    • 0001995554 scopus 로고
    • Mathematical models of the red cell system
    • M. Wazewska-Czyzewska and A. Lasota, Mathematical models of the red cell system, Mat. Stos., 6(1976), 25-40.
    • (1976) Mat. Stos. , vol.6 , pp. 25-40
    • Wazewska-Czyzewska, M.1    Lasota, A.2
  • 23
    • 0031501318 scopus 로고    scopus 로고
    • Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations
    • M. Zennaro, Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations, Numer. Math., 77 (1997), 549-563.
    • (1997) Numer. Math. , vol.77 , pp. 549-563
    • Zennaro, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.