메뉴 건너뛰기




Volumn 42, Issue 5, 2005, Pages 2020-2042

Discretized stability and error growth of the nonautonomous pantograph equation

Author keywords

Asymptotic stability; Error growth; Pantograph equation; Runge Kutta methods

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; NONLINEAR SYSTEMS; RUNGE KUTTA METHODS;

EID: 27744546644     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142902419296     Document Type: Article
Times cited : (31)

References (29)
  • 1
    • 0034515399 scopus 로고    scopus 로고
    • Retarded differential equations
    • C. T. H. BAKER, Retarded differential equations, J. Comput. Appl. Math., 125 (2000), pp. 309-335.
    • (2000) J. Comput. Appl. Math. , vol.125 , pp. 309-335
    • Baker, C.T.H.1
  • 2
    • 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 (1997), pp. 279-293.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 279-293
    • Bellen, A.1    Guglielmi, N.2    Torelli, L.3
  • 3
    • 0034516813 scopus 로고    scopus 로고
    • Numerical stability of nonlinear delay differential equations of neutral type
    • A. BELLEN, N. GUGLIELMI, AND M. ZENNARO, Numerical stability of nonlinear delay differential equations of neutral type, J. Comput. Appl. Math., 125 (2000), pp. 251-263.
    • (2000) J. Comput. Appl. Math. , vol.125 , pp. 251-263
    • Bellen, A.1    Guglielmi, N.2    Zennaro, M.3
  • 4
    • 0346374856 scopus 로고    scopus 로고
    • Contractive initializing methods for the pantograph equation of neutral type
    • A. BELLEN, S. MASET, AND L. TORELLI, Contractive initializing methods for the pantograph equation of neutral type, Recent Trends in Numerical Analysis, 3 (2000), pp. 35-41.
    • (2000) Recent Trends in Numerical Analysis , vol.3 , pp. 35-41
    • Bellen, A.1    Maset, S.2    Torelli, L.3
  • 6
    • 0342489541 scopus 로고
    • Numerical analysis of functional equations with a variable delay
    • Numerical Analysis 1991 Dundee, D. F. Griffiths and G. A. Watson, eds., Longman, Harlow, UK
    • M. D. BUHMANN AND A. ISERLES, Numerical analysis of functional equations with a variable delay, in Numerical Analysis 1991 (Dundee, 1991), D. F. Griffiths and G. A. Watson, eds., Longman, Sci. Tech., Harlow, UK, 1992, pp. 17-33.
    • (1991) Sci. Tech. , pp. 17-33
    • Buhmann, M.D.1    Iserles, A.2
  • 7
    • 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 (1992), pp. 339-363.
    • (1992) IMA J. Numer. Anal. , vol.12 , pp. 339-363
    • Buhmann, M.D.1    Iserles, A.2
  • 8
    • 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 (1993), pp. 575-589.
    • (1993) Math. Comp. , vol.60 , pp. 575-589
    • Buhmann, M.D.1    Iserles, A.2
  • 9
    • 0040132997 scopus 로고
    • Runge-Kutta methods for neutral differential equations
    • Contributions in Numerical Mathematics, World Scientific, River Edge, NJ
    • M. D. BUHMANN, A. ISERLES, AND S. P. NORSETT, Runge-Kutta methods for neutral differential equations, in Contributions in Numerical Mathematics, World Sci. Ser. Appl. Anal. 2, World Scientific, River Edge, NJ, 1993, pp. 85-98.
    • (1993) World Sci. Ser. Appl. Anal. , vol.2 , pp. 85-98
    • Buhmann, M.D.1    Iserles, A.2    Norsett, S.P.3
  • 10
    • 0002351173 scopus 로고
    • Stability criteria for implicit Runge-Kutta methods
    • K. BURRAGE AND J. C. BUTCHER, Stability criteria for implicit Runge-Kutta methods, SIAM J. Numer. Anal., 16 (1979), pp. 46-57.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 46-57
    • Burrage, K.1    Butcher, J.C.2
  • 11
    • 0001356367 scopus 로고
    • Nonlinear stability of a general class of differential equation methods
    • K. BURRAGE AND J. C. BUTCHER, Nonlinear stability of a general class of differential equation methods, BIT, 20 (1980), pp. 185-203.
    • (1980) BIT , vol.20 , pp. 185-203
    • Burrage, K.1    Butcher, J.C.2
  • 12
    • 0003239298 scopus 로고
    • Stability of Runge-Kutta methods for stiff nonlinear differential equations
    • North-Holland, Amsterdam
    • K. DEKKER AND J. G. VERWER, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, CWI Monographs 2, North-Holland, Amsterdam, 1984.
    • (1984) CWI Monographs , vol.2
    • Dekker, K.1    Verwer, J.G.2
  • 13
    • 0038166019 scopus 로고    scopus 로고
    • Stability of one-leg θ-methods for the variable coefficient pantograph equation on the quasi-geometric mesh
    • N. GUGLIELMI AND M. ZENNARO, Stability of one-leg θ-methods for the variable coefficient pantograph equation on the quasi-geometric mesh, IMA J. Numer. Anal., 23 (2003), pp. 421-438.
    • (2003) IMA J. Numer. Anal. , vol.23 , pp. 421-438
    • Guglielmi, N.1    Zennaro, M.2
  • 15
    • 0001129731 scopus 로고    scopus 로고
    • Stability analysis of Runge-Kutta methods for nonlinear delay differential equations
    • C. HUANG, H. Fu, S. Li, AND G. CHEN, Stability analysis of Runge-Kutta methods for nonlinear delay differential equations, BIT, 39 (1999), pp. 270-280.
    • (1999) BIT , vol.39 , pp. 270-280
    • Huang, C.1    Fu, H.2    Li, S.3    Chen, G.4
  • 16
    • 52649085452 scopus 로고
    • On the generalized pantograph functional-differential equations
    • A. ISERLES, On the generalized pantograph functional-differential equations, European J. Appl. Math., 4 (1993), pp. 1-38.
    • (1993) European J. Appl. Math. , vol.4 , pp. 1-38
    • Iserles, A.1
  • 17
    • 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 (1994), pp. 133-152.
    • (1994) Ann. Numer. Math. , vol.1 , pp. 133-152
    • Iserles, A.1
  • 18
    • 0031212296 scopus 로고    scopus 로고
    • Exact and discretized stability of the pantograph equation
    • A. ISERLES, Exact and discretized stability of the pantograph equation, Appl. Numer. Math., 24 (1997), pp. 295-308.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 295-308
    • Iserles, A.1
  • 19
    • 0009028686 scopus 로고
    • Stability and asymptotic stability of functional-differential equations
    • A. ISERLES AND J. TERJEKI, Stability and asymptotic stability of functional-differential equations, J. London Math. Soc. (2), 51 (1995), pp. 559-572.
    • (1995) J. London Math. Soc. (2) , vol.51 , pp. 559-572
    • Iserles, A.1    Terjeki, J.2
  • 20
    • 0001044031 scopus 로고
    • Asymptotic stability analysis of θ-methods for functional differential equations
    • Z. JACKIEWICZ, Asymptotic stability analysis of θ-methods for functional differential equations, Numer. Math., 43 (1984), pp. 389-396.
    • (1984) Numer. Math. , vol.43 , pp. 389-396
    • Jackiewicz, Z.1
  • 21
    • 22844457024 scopus 로고    scopus 로고
    • Stability of Runge-Kutta methods for the generalized pantograph equation
    • T. KOTO, Stability of Runge-Kutta methods for the generalized pantograph equation, Numer. Math., 84 (1999), pp. 233-247.
    • (1999) Numer. Math. , vol.84 , pp. 233-247
    • Koto, T.1
  • 22
    • 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 (1995), pp. 473-485.
    • (1995) Numer. Math. , vol.70 , pp. 473-485
    • Liu, Y.1
  • 23
    • 0030523604 scopus 로고    scopus 로고
    • Asymptotic behaviour of functional-differential equations with proportional time delay
    • Y. Liu, Asymptotic behaviour of functional-differential equations with proportional time delay, European J. Appl. Math., 7 (1996), pp. 11-30.
    • (1996) European J. Appl. Math. , vol.7 , pp. 11-30
    • Liu, Y.1
  • 24
    • 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 (1996), pp. 177-190.
    • (1996) J. Comput. Appl. Math. , vol.71 , pp. 177-190
    • Liu, Y.1
  • 25
    • 0031212297 scopus 로고    scopus 로고
    • Numerical investigation of the pantograph equation
    • Y. Liu, Numerical investigation of the pantograph equation, Appl. Numer. Math., 24 (1997), pp. 309-317.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 309-317
    • Liu, Y.1
  • 26
    • 2942666323 scopus 로고    scopus 로고
    • A stable numerical approach for implicit non-linear neutral delay differential equations
    • R. VERMIGLIO AND L. TORELLI, A stable numerical approach for implicit non-linear neutral delay differential equations, BIT, 43 (2003), pp. 195-C215.
    • (2003) BIT , vol.43
    • Vermiglio, R.1    Torelli, L.2
  • 27
    • 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), pp. 549-563.
    • (1997) Numer. Math. , vol.77 , pp. 549-563
    • Zennaro, M.1
  • 28
    • 1942425045 scopus 로고    scopus 로고
    • Nonlinear stability of variable stepsize Runge-Kutta methods applied to infinite delay-differential equations
    • C. J. ZHANG AND G. SUN, Nonlinear stability of variable stepsize Runge-Kutta methods applied to infinite delay-differential equations, Math. Comput. Modelling, 39 (2004), pp. 495-503.
    • (2004) Math. Comput. Modelling , vol.39 , pp. 495-503
    • Zhang, C.J.1    Sun, G.2
  • 29
    • 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 (2002), pp. 521-526.
    • (2002) Appl. Math. Lett. , vol.15 , pp. 521-526
    • Zhang, C.J.1    Sun, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.