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Volumn 4, Issue 1-2, 2009, Pages 1-9

Forty-five years of A-stability

Author keywords

A stability; Non linear stability; Order arrows; Order stars; Stability barriers; Stiff problems

Indexed keywords


EID: 67650652483     PISSN: 17908140     EISSN: 17908159     Source Type: Journal    
DOI: None     Document Type: Conference Paper
Times cited : (8)

References (15)
  • 1
    • 58249086598 scopus 로고    scopus 로고
    • Order and stability of generalized Padé approximations
    • Butcher J. C., Order and stability of generalized Padé approximations, Appl. Numer. Math. 59 (2009), 558-567.
    • (2009) Appl. Numer. Math , vol.59 , pp. 558-567
    • Butcher, J.C.1
  • 2
    • 0042266154 scopus 로고
    • Generalized Padé approximations to the exponential function
    • Butcher J. C. and Chipman F. H., Generalized Padé approximations to the exponential function, BIT, 32 (1992), 118-130.
    • (1992) BIT , vol.32 , pp. 118-130
    • Butcher, J.C.1    Chipman, F.H.2
  • 3
    • 33645038609 scopus 로고    scopus 로고
    • Linear multistep methods as irreducible general linear methods
    • Butcher J. C. and Hill A. T, Linear multistep methods as irreducible general linear methods, BIT, 46 (2006), 5-19.
    • (2006) BIT , vol.46 , pp. 5-19
    • Butcher, J.C.1    Hill, A.T.2
  • 4
    • 0002211850 scopus 로고
    • Stability of Runge-Kutta methods for trajectory problems
    • Cooper G. J., Stability of Runge-Kutta methods for trajectory problems, IMA J. Numer. Anal., 7 (1987), 1-13.
    • (1987) IMA J. Numer. Anal , vol.7 , pp. 1-13
    • Cooper, G.J.1
  • 6
    • 11044230975 scopus 로고
    • A special stability problem for linear multistep methods
    • Dahlquist G., A special stability problem for linear multistep methods, BIT, 3 (1963), 27-43.
    • (1963) BIT , vol.3 , pp. 27-43
    • Dahlquist, G.1
  • 7
    • 0002945485 scopus 로고
    • Error analysis for a class of methods for stiff non-linear initial value problems
    • Dahlquist G., Error analysis for a class of methods for stiff non-linear initial value problems, Lecture Notes in Math., 506 (1976), 60-72.
    • (1976) Lecture Notes in Math , vol.506 , pp. 60-72
    • Dahlquist, G.1
  • 8
    • 0000005117 scopus 로고
    • G-stability is equivalent to A-stability
    • Dahlquist G., G-stability is equivalent to A-stability, BIT, 18 (1978), 384-401.
    • (1978) BIT , vol.18 , pp. 384-401
    • Dahlquist, G.1
  • 10
    • 0039411239 scopus 로고
    • A-stable methods and Padé approximations to the exponential
    • Ehle B. L., A-stable methods and Padé approximations to the exponential SIAM J. Math. Anal., 4 (1973),. 671-680.
    • (1973) SIAM J. Math. Anal , vol.4 , pp. 671-680
    • Ehle, B.L.1
  • 12
    • 84968497765 scopus 로고
    • On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations
    • Prothero A. and Robinson A., On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations, Math. Comp., 28 (1974), 145-162.
    • (1974) Math. Comp , vol.28 , pp. 145-162
    • Prothero, A.1    Robinson, A.2
  • 13
    • 0038976122 scopus 로고
    • Runge-Kutta schemes for Hamiltonian systems
    • Sanz-Serna, J. M., Runge-Kutta schemes for Hamiltonian systems, BIT, 28 (1988), 877-883.
    • (1988) BIT , vol.28 , pp. 877-883
    • Sanz-Serna, J.M.1
  • 14
    • 31644432026 scopus 로고
    • Order stars and stability theorems
    • Wanner G., Hairer E. and Nørsett S. P., Order stars and stability theorems, BIT, 18 (1978), 475-489.
    • (1978) BIT , vol.18 , pp. 475-489
    • Wanner, G.1    Hairer, E.2    Nørsett, S.P.3
  • 15
    • 0009419915 scopus 로고
    • A note on unconditionally stable linear multistep methods
    • Widlund O. B., A note on unconditionally stable linear multistep methods, BIT 7 (1967), 65-70.
    • (1967) BIT , vol.7 , pp. 65-70
    • Widlund, O.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.