메뉴 건너뛰기




Volumn 39, Issue 4-5, 2004, Pages 495-503

Nonlinear stability of Runge-Kutta methods applied to infinite-delay- differential equations

Author keywords

Infinite delay differential equations; Nonlinear stability; Runge Kutta methods

Indexed keywords


EID: 1942425045     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(04)90520-1     Document Type: Article
Times cited : (20)

References (18)
  • 1
    • 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, 549-563, (1997).
    • (1997) Numer. Math. , vol.77 , pp. 549-563
    • Zennaro, M.1
  • 3
    • 0038948786 scopus 로고
    • On the dynamics of a discretized neutral equation
    • M.D. Buhmann and A. Iserles, On the dynamics of a discretized neutral equation, IMA J. Numer. Anal. 12, 339-363, (1992).
    • (1992) IMA J. Numer. Anal. , vol.12 , pp. 339-363
    • Buhmann, M.D.1    Iserles, A.2
  • 4
    • 84968503713 scopus 로고
    • Stability of the discretized pantograph differential equation
    • M.D. Buhmann and A. Iserles, Stability of the discretized pantograph differential equation, Math. Comp. 60, 575-589, (1993).
    • (1993) Math. Comp. , vol.60 , pp. 575-589
    • Buhmann, M.D.1    Iserles, A.2
  • 5
    • 0242709242 scopus 로고
    • Numerical analysis of delay differential equations with variable delays
    • A. Iserles, Numerical analysis of delay differential equations with variable delays, Ann. Numer. Math. 1, 133-152, (1994).
    • (1994) Ann. Numer. Math. , vol.1 , pp. 133-152
    • Iserles, A.1
  • 6
    • 21844488753 scopus 로고
    • Stability analysis of θ-methods for neutral functional-differential equations
    • Y. Liu, Stability analysis of θ-methods for neutral functional-differential equations, Numer. Math. 70, 473-485, (1995).
    • (1995) Numer. Math. , vol.70 , pp. 473-485
    • Liu, Y.1
  • 7
    • 0030194116 scopus 로고    scopus 로고
    • On the θ-methods for delay differential equations with infinite lag
    • Y. Liu, On the θ-methods for delay differential equations with infinite lag, J. Comput. Appl. Math. 71, 177-190, (1996).
    • (1996) J. Comput. Appl. Math. , vol.71 , pp. 177-190
    • Liu, Y.1
  • 8
    • 0031211264 scopus 로고    scopus 로고
    • Asymptotic stability properties of θ-methods for the pantograph equation
    • A. Bellen, N. Guglielmi and L. Torelli, Asymptotic stability properties of θ-methods for the pantograph equation, Appl. Numer. Math. 24, 279-293, (1997).
    • (1997) Appl. Numer. Math. , vol.24 , pp. 279-293
    • Bellen, A.1    Guglielmi, N.2    Torelli, L.3
  • 9
    • 0031212296 scopus 로고    scopus 로고
    • Exact and discretized stbility of the pantograph equation
    • A. Iserles, Exact and discretized stbility of the pantograph equation, Appl. Numer. Math. 24, 295-308, (1997).
    • (1997) Appl. Numer. Math. , vol.24 , pp. 295-308
    • Iserles, A.1
  • 10
    • 38249024166 scopus 로고
    • Stability of numerical methods for delay differential equations
    • L. Torelli, Stability of numerical methods for delay differential equations, J. Comput. Appl. Math. 25, 15-26, (1989).
    • (1989) J. Comput. Appl. Math. , vol.25 , pp. 15-26
    • Torelli, L.1
  • 11
    • 38249014185 scopus 로고
    • Strong contractivity properties of numerical methods for ordinary and delay differential equations
    • A. Bellen and M. Zennaro, Strong contractivity properties of numerical methods for ordinary and delay differential equations, Appl. Numer. Math. 9, 321-346, (1992).
    • (1992) Appl. Numer. Math. , vol.9 , pp. 321-346
    • Bellen, A.1    Zennaro, M.2
  • 12
    • 38249006326 scopus 로고
    • Contractivity of Runge-Kutta methods with respect to forcing terms
    • M. Zennaro, Contractivity of Runge-Kutta methods with respect to forcing terms, Appl. Numer. Math. 10, 321-345, (1993).
    • (1993) Appl. Numer. Math. , vol.10 , pp. 321-345
    • Zennaro, M.1
  • 13
    • 0031276989 scopus 로고    scopus 로고
    • Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations
    • C.J. Zhang and S.Z. Zhou, Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations, J. Comput. Appl. Math. 85, 225-237, (1997).
    • (1997) J. Comput. Appl. Math. , vol.85 , pp. 225-237
    • Zhang, C.J.1    Zhou, S.Z.2
  • 14
    • 0001129731 scopus 로고    scopus 로고
    • Stability analysis of Runge-Kutta methods for nonlinear delay differential equations
    • C.M. Huang, H.Y. Fu, S.F. Li and G.N. Chen, Stability analysis of Runge-Kutta methods for nonlinear delay differential equations, BIT 39, 270-280, (1999).
    • (1999) BIT , vol.39 , pp. 270-280
    • Huang, C.M.1    Fu, H.Y.2    Li, S.F.3    Chen, G.N.4
  • 15
    • 0033097062 scopus 로고    scopus 로고
    • Stability and error analysis of one-leg methods for nonlinear delay differential equations
    • C.M. Huang, S.F. Li, H.Y. Fu and G.N. Chen, Stability and error analysis of one-leg methods for nonlinear delay differential equations, J. Comput. Appl. Math. 103, 263-279, (1999).
    • (1999) J. Comput. Appl. Math. , vol.103 , pp. 263-279
    • Huang, C.M.1    Li, S.F.2    Fu, H.Y.3    Chen, G.N.4
  • 16
    • 31244435236 scopus 로고    scopus 로고
    • The discrete dynamics of nonlinear infinite-delay-differential equations
    • C.J. Zhang and G. Sun, The discrete dynamics of nonlinear infinite-delay-differential equations, Appl. Math. Lett. 15 (5), 521-526, (2002).
    • (2002) Appl. Math. Lett. , vol.15 , Issue.5 , pp. 521-526
    • Zhang, C.J.1    Sun, G.2
  • 17
    • 0001356367 scopus 로고
    • Nonlinear stability of a general class of differential equations methods
    • K. Burrage and J.C. Butcher, Nonlinear stability of a general class of differential equations methods, BIT 20, 185-203, (1980).
    • (1980) BIT , vol.20 , pp. 185-203
    • Burrage, K.1    Butcher, J.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.