메뉴 건너뛰기




Volumn 46, Issue 3, 2006, Pages 479-489

Thirty years of G-stability

Author keywords

A stability; G stability; One leg methods; Stiff problems

Indexed keywords


EID: 33748991151     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-006-0078-8     Document Type: Article
Times cited : (19)

References (22)
  • 1
    • 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
  • 2
    • 0001356367 scopus 로고
    • Non-linear stability of a general class of differential equation methods
    • K. Burrage and J. C. Butcher, Non-linear 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
  • 3
    • 84968505795 scopus 로고
    • On the convergence of numerical solutions of ordinary differential equations
    • J. C. Butcher, On the convergence of numerical solutions of ordinary differential equations, Math. Comp., 20 (1966), pp. 1-10.
    • (1966) Math. Comp. , vol.20 , pp. 1-10
    • Butcher, J.C.1
  • 4
    • 0016647175 scopus 로고
    • A stability property of implicit Runge-Kutta methods
    • J. C. Butcher, A stability property of implicit Runge-Kutta methods, BIT, 15 (1975), pp. 358-361.
    • (1975) BIT , vol.15 , pp. 358-361
    • Butcher, J.C.1
  • 5
    • 1542666003 scopus 로고
    • Linear and non-linear stability for general linear methods
    • J. C. Butcher, Linear and non-linear stability for general linear methods, BIT, 27 (1987), pp. 182-189.
    • (1987) BIT , vol.27 , pp. 182-189
    • Butcher, J.C.1
  • 6
    • 33645019289 scopus 로고
    • The equivalence of algebraic stability and AN-stability
    • J. C. Butcher, The equivalence of algebraic stability and AN-stability, BIT, 27 (1987), pp. 510-533.
    • (1987) BIT , vol.27 , pp. 510-533
    • Butcher, J.C.1
  • 7
    • 33645038609 scopus 로고    scopus 로고
    • Linear multistep methods as irreducible general linear methods
    • J. C. Butcher and A. T. Hill, Linear multistep methods as irreducible general linear methods, BIT, 46 (2006), pp. 5-19.
    • (2006) BIT , vol.46 , pp. 5-19
    • Butcher, J.C.1    Hill, A.T.2
  • 8
    • 0002089844 scopus 로고
    • Sur la B-stabilité des méthodes de Runge-Kutta
    • M. Crouzeix, Sur la B-stabilité des méthodes de Runge-Kutta, Numer. Math., 32 (1979), pp. 75-82.
    • (1979) Numer. Math. , vol.32 , pp. 75-82
    • Crouzeix, M.1
  • 10
    • 0011566457 scopus 로고
    • Convergence and stability in the numerical integration of ordinary differential equations
    • G. Dahlquist, Convergence and stability in the numerical integration of ordinary differential equations, Math. Scand., 4 (1956), pp. 33-53.
    • (1956) Math. Scand. , vol.4 , pp. 33-53
    • Dahlquist, G.1
  • 11
    • 11044230975 scopus 로고
    • A special stability problem for linear multistep methods
    • G. Dahlquist, A special stability problem for linear multistep methods, BIT, 3 (1963), pp. 27-43.
    • (1963) BIT , vol.3 , pp. 27-43
    • Dahlquist, G.1
  • 12
    • 33749035042 scopus 로고
    • On stability and error analysis for stiff non-linear problems, 1
    • Dept of Information Processing, Royal Institute of Technology, Stockholm
    • G. Dahlquist, On stability and error analysis for stiff non-linear problems, 1, Dept of Information Processing, Royal Institute of Technology, Stockholm, Report NA 75.08 (1975).
    • (1975) Report NA 75.08
    • Dahlquist, G.1
  • 13
    • 0002945485 scopus 로고
    • Error analysis for a class of methods for stiff nonlinear initial value problems
    • Proc. Numer. Anal. Conf., Dundee, Scotland, 1975, Springer, New York
    • G. Dahlquist, Error analysis for a class of methods for stiff nonlinear initial value problems, Proc. Numer. Anal. Conf., Dundee, Scotland, 1975, Lecture Notes Math., vol. 506, pp. 60-74, Springer, New York, 1976.
    • (1976) Lecture Notes Math. , vol.506 , pp. 60-74
    • Dahlquist, G.1
  • 14
    • 0000005117 scopus 로고
    • G-stability is equivalent to A-stability
    • G. Dahlquist, G-stability is equivalent to A-stability, BIT, 18 (1978), pp. 384-401.
    • (1978) BIT , vol.18 , pp. 384-401
    • Dahlquist, G.1
  • 15
    • 0346498559 scopus 로고
    • Stability of two-step methods for variable integration steps
    • G. Dahlquist, W. Liniger, and O. Nevanlinna, Stability of two-step methods for variable integration steps, SIAM J. Numer. Anal., 20 (1983), pp. 1071-1085.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 1071-1085
    • Dahlquist, G.1    Liniger, W.2    Nevanlinna, O.3
  • 16
    • 33645035250 scopus 로고
    • Some problems related to stiff nonlinear differential systems
    • R. Glowinski, J. L. Lions, eds., North Holland, Amsterdam
    • G. Dahlquist and G. Söderlind, Some problems related to stiff nonlinear differential systems, in Computing methods in Applied Sciences and Engineering V, R. Glowinski, J. L. Lions, eds., pp. 57-74, North Holland, Amsterdam, 1982.
    • (1982) Computing Methods in Applied Sciences and Engineering v , pp. 57-74
    • Dahlquist, G.1    Söderlind, G.2
  • 18
    • 0011615763 scopus 로고
    • Canonical Runge-Kutta methods
    • F. Lasagni, Canonical Runge-Kutta methods, Z. Angew. Math. Phys., 39 (1988), pp. 952-953.
    • (1988) Z. Angew. Math. Phys. , vol.39 , pp. 952-953
    • Lasagni, F.1
  • 19
    • 0019669231 scopus 로고
    • Multiplier techniques for linear multistep methods
    • O. Nevanlinna and F. Odeh, Multiplier techniques for linear multistep methods, Numer. Funct. Anal. Optim., 3 (1981), pp. 377-123.
    • (1981) Numer. Funct. Anal. Optim. , vol.3 , pp. 377-1123
    • Nevanlinna, O.1    Odeh, F.2
  • 20
    • 0038976122 scopus 로고
    • Runge-Kutta schemes for Hamiltonian systems
    • J. M. Sanz-Serna, Runge-Kutta schemes for Hamiltonian systems, BIT, 28 (1988), pp. 877-883.
    • (1988) BIT , vol.28 , pp. 877-883
    • Sanz-Serna, J.M.1
  • 21
    • 84971897259 scopus 로고
    • Symplectic integrators for Hamiltonian problems: An overview
    • J. M. Sanz-Serna, Symplectic integrators for Hamiltonian problems: an overview, Acta Numer., 1 (1991), pp. 243-286.
    • (1991) Acta Numer. , vol.1 , pp. 243-286
    • Sanz-Serna, J.M.1
  • 22
    • 0037747984 scopus 로고
    • Canonical transformations generated by methods of Runge-Kutta type for the numerical integration for the system x = -∂U/∂x
    • in Russian
    • Y. B. Suris, Canonical transformations generated by methods of Runge-Kutta type for the numerical integration for the system x = -∂U/∂x, Zh. Vychisl. Mat. i Mat. Fiz., 29 (1989), pp. 202-211 (in Russian).
    • (1989) Zh. Vychisl. Mat. i Mat. Fiz. , vol.29 , pp. 202-211
    • Suris, Y.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.