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Volumn 24, Issue 2, 2004, Pages 193-214

Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations

Author keywords

Compound quadrature; Pouzet quadrature; Runge Kutta methods; Stability; Volterra delay integro differential equations

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; INTEGRODIFFERENTIAL EQUATIONS; NONLINEAR EQUATIONS; STABILITY CRITERIA;

EID: 2942653262     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/24.2.193     Document Type: Article
Times cited : (73)

References (21)
  • 1
    • 0034517076 scopus 로고    scopus 로고
    • A perspective on the numerical treatment of Volterra equations
    • BAKER, C. T. H. (2000) A perspective on the numerical treatment of Volterra equations. J. Comput. Appl. Math., 125, 217-249.
    • (2000) J. Comput. Appl. Math. , vol.125 , pp. 217-249
    • Baker, C.T.H.1
  • 2
    • 38249015918 scopus 로고
    • Stability properties of a scheme for the approximate solution of a delay integro-differential equation
    • BAKER, C. T. H. & FORD, N. J. (1992) Stability properties of a scheme for the approximate solution of a delay integro-differential equation. Appl. Numer. Math., 9, 357-370.
    • (1992) Appl. Numer. Math. , vol.9 , pp. 357-370
    • Baker, C.T.H.1    Ford, N.J.2
  • 3
    • 2142732543 scopus 로고
    • Convergence of linear multistep methods for a class of delay-integro-differential equations
    • Basel: Birkhauser
    • BAKER, C. T. H. & FORD, N. J. (1988) Convergence of linear multistep methods for a class of delay-integro-differential equations. International Series of Numerical Mathematics, Vol. 86. Basel: Birkhauser, pp. 47-59.
    • (1988) International Series of Numerical Mathematics , vol.86 , pp. 47-59
    • Baker, C.T.H.1    Ford, N.J.2
  • 4
    • 0031207491 scopus 로고    scopus 로고
    • Stability analysis of continuous implicit Runge-Kutta methods for Volterra integro-differential equations systems with unbound delays
    • BAKER, C. T. H. & TANG, A. (1997) Stability analysis of continuous implicit Runge-Kutta methods for Volterra integro-differential equations systems with unbound delays. Appl. Numer. Math., 24, 153-173.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 153-173
    • Baker, C.T.H.1    Tang, A.2
  • 5
    • 38249014185 scopus 로고
    • Strong connectivity properties of numerical methods for ordinary and delay differential equations
    • BELLEN, A. & ZENNARO, M. (1992) Strong connectivity properties of numerical methods for ordinary and delay differential equations. Appl. Numer. Math., 9, 321-346.
    • (1992) Appl. Numer. Math. , vol.9 , pp. 321-346
    • Bellen, A.1    Zennaro, M.2
  • 7
    • 0034509077 scopus 로고    scopus 로고
    • Numerical modelling in biosciences delay differential equations
    • BOCHARAROV, G. A. & RIHAN, A. (2000) Numerical modelling in biosciences delay differential equations. J. Comput. Appl. Math., 125, 183-199.
    • (2000) J. Comput. Appl. Math. , vol.125 , pp. 183-199
    • Bochararov, G.A.1    Rihan, A.2
  • 8
    • 0005566582 scopus 로고
    • The numerical solution of neutral Volterra integro-differential equations with delay arguments
    • BRUNNER, H. (1994) The numerical solution of neutral Volterra integro-differential equations with delay arguments. Ann. Numer. Math., 1, 309-322.
    • (1994) Ann. Numer. Math. , vol.1 , pp. 309-322
    • Brunner, H.1
  • 10
    • 0001356367 scopus 로고
    • Nonlinear stability of a general class of differential equations methods
    • BURRAGE, K. & BUTCHER, J. C. (1980) Nonlinear stability of a general class of differential equations methods. BIT, 20, 185-203.
    • (1980) BIT , vol.20 , pp. 185-203
    • Burrage, K.1    Butcher, J.C.2
  • 11
    • 0031212295 scopus 로고    scopus 로고
    • Continous Runge-Kutta methods for neutral Volterra integro-differential equations with delay
    • ENRIGHT, W. H. & HU, M. (1997) Continous Runge-Kutta methods for neutral Volterra integro-differential equations with delay. Appl. Numer. Math., 24, 175-190.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 175-190
    • Enright, W.H.1    Hu, M.2
  • 13
    • 0001129731 scopus 로고    scopus 로고
    • Stability analysis of Runge-Kutta methods for non-linear delay differential equations
    • HUANG, C., FU, H., LI, S. & CHEN, G. (1999) Stability analysis of Runge-Kutta methods for non-linear delay differential equations. BIT, 39, 270-280.
    • (1999) BIT , vol.39 , pp. 270-280
    • Huang, C.1    Fu, H.2    Li, S.3    Chen, G.4
  • 14
    • 6344235484 scopus 로고    scopus 로고
    • An analysis of delay-dependent stability for ordinary and partial differential equations with fixed and distributed delays
    • to appear
    • HUANG, C. & VANDEWALLE, S. (2003) An analysis of delay-dependent stability for ordinary and partial differential equations with fixed and distributed delays. SIAM J. Sci. Comput., to appear.
    • (2003) SIAM J. Sci. Comput.
    • Huang, C.1    Vandewalle, S.2
  • 15
    • 0037102575 scopus 로고    scopus 로고
    • Stability of Runge-Kutta methods for delay integro-differential equations
    • KOTO, T. (2002) Stability of Runge-Kutta methods for delay Integro-differential equations. J. Comput. Appl. Math., 145, 483-492.
    • (2002) J. Comput. Appl. Math. , vol.145 , pp. 483-492
    • Koto, T.1
  • 17
    • 0347093579 scopus 로고    scopus 로고
    • Computing stability of differential equations with bounded and distributed delays
    • LUZYANINA, T., ENGELBORGHS, K. & ROOSE, D. (2003) Computing stability of differential equations with bounded and distributed delays. Numer. Algorithms, 34, 41-66.
    • (2003) Numer. Algorithms , vol.34 , pp. 41-66
    • Luzyanina, T.1    Engelborghs, K.2    Roose, D.3
  • 18
    • 2942675151 scopus 로고
    • Sur la B-stabilité pour une équation différentielle á retard
    • REVERDY, J. (1990) Sur la B-stabilité pour une équation différentielle á retard. C. R. Acad. Sci. Paris Sér. I Math., 310, 461-463.
    • (1990) C. R. Acad. Sci. Paris Sér. I Math. , vol.310 , pp. 461-463
    • Reverdy, J.1
  • 19
    • 38249024166 scopus 로고
    • Stability of numerical methods for delay differential equations
    • TORELLI, L. (1989) Stability of numerical methods for delay differential equations. J. Comput. Appl. Math., 25, 15-26.
    • (1989) J. Comput. Appl. Math. , vol.25 , pp. 15-26
    • Torelli, L.1
  • 20
    • 0031501318 scopus 로고    scopus 로고
    • Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations
    • ZENNARO, M. (1997) Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations. Numer. Math., 77, 549-563.
    • (1997) Numer. Math. , vol.77 , pp. 549-563
    • Zennaro, M.1
  • 21
    • 4043178915 scopus 로고    scopus 로고
    • Stability analysis of delay-integro-differential equations and their backward differentiation time-discretization
    • to appear
    • ZHANG, C. & VANDEWALLE, S. (2003) Stability analysis of delay-integro-differential equations and their backward differentiation time-discretization. J. Comput. Appl. Math., to appear.
    • (2003) J. Comput. Appl. Math.
    • Zhang, C.1    Vandewalle, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.