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Volumn 54, Issue 9-10, 2011, Pages 2493-2503

Stability of delay integro-differential equations using a spectral element method

Author keywords

Delay equations; Delay integro differential equations; Spectral element; Stability

Indexed keywords

DELAY DIFFERENTIAL EQUATIONS; DELAY EQUATIONS; DISCRETE DELAY; DISTRIBUTED DELAYS; HIGHER ORDER; INFINITE DIMENSIONAL; INTEGRAL TERMS; KERNEL FUNCTION; NONAUTONOMOUS; PRACTICAL IMPORTANCE; SPECTRAL ELEMENT; SPECTRAL ELEMENT METHOD; STABILITY ANALYSIS; STATE-SPACE;

EID: 80051585496     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2011.06.009     Document Type: Article
Times cited : (27)

References (29)
  • 1
    • 44849140940 scopus 로고    scopus 로고
    • Delay nonlinear oscillations and shimmying wheels
    • Kluwer Academic Publisher, Dordrecht, F.C. Moon (Ed.)
    • Stépán G. Delay nonlinear oscillations and shimmying wheels. Applications of Nonlinear and Chaotic Dynamics in Mechanics 1998, 373-386. Kluwer Academic Publisher, Dordrecht. 1st ed. F.C. Moon (Ed.).
    • (1998) Applications of Nonlinear and Chaotic Dynamics in Mechanics , pp. 373-386
    • Stépán, G.1
  • 2
    • 39749154638 scopus 로고    scopus 로고
    • Isolated large amplitude periodic motions of towed rigid wheels
    • Takács D., Stépán G., Hogan S.J. Isolated large amplitude periodic motions of towed rigid wheels. Nonlinear Dynamics 2007, 52(1):27-34.
    • (2007) Nonlinear Dynamics , vol.52 , Issue.1 , pp. 27-34
    • Takács, D.1    Stépán, G.2    Hogan, S.J.3
  • 3
    • 60449098800 scopus 로고    scopus 로고
    • Delay effects in shimmy dynamics of wheels with stretched string-like tyres
    • Takács D., Orosz G., Stépán G. Delay effects in shimmy dynamics of wheels with stretched string-like tyres. European Journal of Mechanics-A/Solids 2009, 28(3):516-525. 10.1016/j.euromechsol.2008.11.007.
    • (2009) European Journal of Mechanics-A/Solids , vol.28 , Issue.3 , pp. 516-525
    • Takács, D.1    Orosz, G.2    Stépán, G.3
  • 4
    • 0001407970 scopus 로고    scopus 로고
    • Analysis of optimal velocity model with explicit delay
    • Bando M., Hasebe K., Nakanishi K., Nakayama A. Analysis of optimal velocity model with explicit delay. Physical Review E 1998, 58(5):5429-5435. 10.1103/PhysRevE.58.5429.
    • (1998) Physical Review E , vol.58 , Issue.5 , pp. 5429-5435
    • Bando, M.1    Hasebe, K.2    Nakanishi, K.3    Nakayama, A.4
  • 5
    • 42749102192 scopus 로고    scopus 로고
    • Global bifurcation investigation of an optimal velocity traffic model with driver reaction time
    • Orosz G., Wilson R., Krauskopf B. Global bifurcation investigation of an optimal velocity traffic model with driver reaction time. Physical Review E 2004, 70(2):026207. 10.1103/PhysRevE.70.026207.
    • (2004) Physical Review E , vol.70 , Issue.2 , pp. 026207
    • Orosz, G.1    Wilson, R.2    Krauskopf, B.3
  • 6
    • 33748103156 scopus 로고    scopus 로고
    • Subcritical hopf bifurcations in a car-following model with reaction-time delay
    • Orosz G., Stépán G. Subcritical hopf bifurcations in a car-following model with reaction-time delay. Proceedings of the Royal Society A 2006, 462(2073):2643-2670. 10.1098/rspa.2006.1660.
    • (2006) Proceedings of the Royal Society A , vol.462 , Issue.2073 , pp. 2643-2670
    • Orosz, G.1    Stépán, G.2
  • 7
    • 47149084701 scopus 로고    scopus 로고
    • Stability of traffic flow behavior with distributed delays modeling the memory effects of the drivers
    • Sipahi R., Atay F., Niculescu S.-I. Stability of traffic flow behavior with distributed delays modeling the memory effects of the drivers. SIAM Journal of Applied Mathematics 2007, 68(3):738-759. 10.1137/060673813.
    • (2007) SIAM Journal of Applied Mathematics , vol.68 , Issue.3 , pp. 738-759
    • Sipahi, R.1    Atay, F.2    Niculescu, S.-I.3
  • 8
    • 60349084549 scopus 로고    scopus 로고
    • Consensus problems with distributed delays, with application to traffic flow models
    • Michiels W., Morǎrescu C.-I., Niculescu S.-I. Consensus problems with distributed delays, with application to traffic flow models. SIAM Journal on Control and Optimization 2009, 48(1):77-101. 10.1137/060671425.
    • (2009) SIAM Journal on Control and Optimization , vol.48 , Issue.1 , pp. 77-101
    • Michiels, W.1    Morǎrescu, C.-I.2    Niculescu, S.-I.3
  • 11
    • 34548139371 scopus 로고    scopus 로고
    • Time delays in neural systems
    • Springer-Verlag.
    • Campbell S. Time delays in neural systems. Handbook of Brain Connectivity 2007, Springer-Verlag, pp. 65-90.
    • (2007) Handbook of Brain Connectivity , pp. 65-90
    • Campbell, S.1
  • 12
    • 0037102575 scopus 로고    scopus 로고
    • Stability of Runge-Kutta methods for delay integro-differential equations
    • Koto T. Stability of Runge-Kutta methods for delay integro-differential equations. Journal of Computational and Applied Mathematics 2002, 145(2):483-492. 10.1016/S0377-0427(01)00596-9.
    • (2002) Journal of Computational and Applied Mathematics , vol.145 , Issue.2 , pp. 483-492
    • Koto, T.1
  • 13
    • 2942653262 scopus 로고    scopus 로고
    • Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations
    • Zhang C., Vandewalle S. Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. IMA Journal of Numerical Analysis 2004, 24:193-214. (22).
    • (2004) IMA Journal of Numerical Analysis , vol.24 , Issue.22 , pp. 193-214
    • Zhang, C.1    Vandewalle, S.2
  • 14
    • 38249015918 scopus 로고
    • Stability properties of a scheme for the approximate solution of a delay-integro-differential equation
    • Baker C., Ford N. Stability properties of a scheme for the approximate solution of a delay-integro-differential equation. Applied Numerical Mathematics 1992, 9(3-5):357-370. 10.1016/0168-9274(92)90027-B.
    • (1992) Applied Numerical Mathematics , vol.9 , Issue.3-5 , pp. 357-370
    • Baker, C.1    Ford, N.2
  • 15
    • 0347093579 scopus 로고    scopus 로고
    • Computing stability of differential equations with bounded distributed delays
    • Luzyanina T., Engelborghs K., Roose D. Computing stability of differential equations with bounded distributed delays. Numerical Algorithms 2003, 34(1):41-66. 10.1023/A:1026194503720.
    • (2003) Numerical Algorithms , vol.34 , Issue.1 , pp. 41-66
    • Luzyanina, T.1    Engelborghs, K.2    Roose, D.3
  • 16
    • 17644365001 scopus 로고    scopus 로고
    • Equations with distributed delays: bifurcation analysis using computational tools for discrete delay equations
    • Luzyanina T., Roose D. Equations with distributed delays: bifurcation analysis using computational tools for discrete delay equations. Functional Differential Equations 2004, 11(1-2):87-92.
    • (2004) Functional Differential Equations , vol.11 , Issue.1-2 , pp. 87-92
    • Luzyanina, T.1    Roose, D.2
  • 17
    • 77951101757 scopus 로고    scopus 로고
    • Stability implications of delay distribution for first-order and second-order systems
    • Kiss G., Krauskopf B. Stability implications of delay distribution for first-order and second-order systems. Discrete and Continuous Dynamical Systems-series B 2010, 13(2):327-345. 10.3934/dcdsb.2010.13.327.
    • (2010) Discrete and Continuous Dynamical Systems-series B , vol.13 , Issue.2 , pp. 327-345
    • Kiss, G.1    Krauskopf, B.2
  • 18
    • 79951816267 scopus 로고    scopus 로고
    • Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback
    • Kiss G., Krauskopf B. Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback. Dynamical Systems: An International Journal 2011, 26(1):85-101. 10.1080/14689367.2010.523889.
    • (2011) Dynamical Systems: An International Journal , vol.26 , Issue.1 , pp. 85-101
    • Kiss, G.1    Krauskopf, B.2
  • 20
    • 40949113761 scopus 로고    scopus 로고
    • On the higher-order semi-discretizations for periodic delayed systems
    • Insperger T., Stépán G., Turi J. On the higher-order semi-discretizations for periodic delayed systems. Journal of Sound and Vibration 2008, 313:334-341.
    • (2008) Journal of Sound and Vibration , vol.313 , pp. 334-341
    • Insperger, T.1    Stépán, G.2    Turi, J.3
  • 21
    • 1642580774 scopus 로고    scopus 로고
    • Computing the characteristic roots for delay differential equations
    • Breda D., Maset S., Vermiglio R. Computing the characteristic roots for delay differential equations. IMA Journal of Numerical Analysis 2004, 24(1):1-19. 10.1093/imanum/24.1.1.
    • (2004) IMA Journal of Numerical Analysis , vol.24 , Issue.1 , pp. 1-19
    • Breda, D.1    Maset, S.2    Vermiglio, R.3
  • 24
    • 4944240756 scopus 로고    scopus 로고
    • Barycentric Lagrange interpolation
    • Berrut J., Trefethen L.N. Barycentric Lagrange interpolation. SIAM Review 2004, 46(3):501-517.
    • (2004) SIAM Review , vol.46 , Issue.3 , pp. 501-517
    • Berrut, J.1    Trefethen, L.N.2
  • 25
    • 7444229866 scopus 로고    scopus 로고
    • The numerical stability of Barycentric Lagrange interpolation
    • arXiv:
    • Higham N. The numerical stability of Barycentric Lagrange interpolation. IMA Journal of Numerical Analysis 2004, 24(4):547-556. arXiv:http://imajna.oxfordjournals.org/cgi/reprint/24/4/547.pdf. 10.1093/imanum/24.4.547.
    • (2004) IMA Journal of Numerical Analysis , vol.24 , Issue.4 , pp. 547-556
    • Higham, N.1
  • 26
    • 0036627555 scopus 로고    scopus 로고
    • Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations
    • Engelborghs K., Doedel E. Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations. Numerische Mathematik 2002, 91:627-648.
    • (2002) Numerische Mathematik , vol.91 , pp. 627-648
    • Engelborghs, K.1    Doedel, E.2
  • 28
    • 70349910083 scopus 로고    scopus 로고
    • Explanation for low-speed stability increases in machining: application of a continuous delay model, in: Proceedings of the ASME 2008 Dynamic Systems and Control Conference, Invited Session on "Time-Delay Systems, from Theory to Applications", October 20-20 2008, Ann Arbor, Michigan, USA, No. DSCC2008-2287.
    • F. Khasawneh, B. Mann, T. Insperger, G. Stépán, Explanation for low-speed stability increases in machining: application of a continuous delay model, in: Proceedings of the ASME 2008 Dynamic Systems and Control Conference, Invited Session on "Time-Delay Systems, from Theory to Applications", October 20-22, 2008, Ann Arbor, Michigan, USA, No. DSCC2008-2287, 2008.
    • (2008)
    • Khasawneh, F.1    Mann, B.2    Insperger, T.3    Stépán, G.4
  • 29
    • 21344442580 scopus 로고    scopus 로고
    • On the problem of linearization for state-dependent delay differential equations
    • Cooke K., Huang W. On the problem of linearization for state-dependent delay differential equations. Proceedings of the American Mathematical Society 1996, 124(5):1417-1426.
    • (1996) Proceedings of the American Mathematical Society , vol.124 , Issue.5 , pp. 1417-1426
    • Cooke, K.1    Huang, W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.