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G-stability is equivalent to A-stability. (English) Zbl 0413.65057

MSC:
65L07 Numerical investigation of stability of solutions to ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
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[1] K. Burrage and J. C. Butcher,Stability Criteria for Implicit Runge-Kutta Methods, University of Auckland, Dept. of Math., Report no 117 (1977). · Zbl 0396.65043
[2] G. Dahlquist,On One-leg Methods and their Relation to Linear Multistep Methods, to appear. · Zbl 0529.65048
[3] G. Dahlquist,A Special Stability Problem for Linear Multistep Methods, BIT 3 (1963), 27–43. · Zbl 0123.11703
[4] G. Dahlquist,On Stability and Error Analysis for Stiff Non-linear Problems, Part I, Royal Inst. of Technology, Stockholm, Report TRITA-NA-7508 (1975).
[5] G. Dahlquist,Error Analysis for a Class of Methods of Stiff Non-linear Initial Value Problems, Numerical Analysis, Dundee 1975, Springer Lecture Notes in Mathematics, nr. 506 (1975), 60–74.
[6] G. Dahlquist,On the Relation of G-stability to Other Concepts for Linear Multistep Methods, Topics in Numerical Analysis III, 67–80, ed. J. H. Miller, Acad. Press, London (1977).
[7] G. Dahlquist,Positive Functions and Some Applications to Stability Questions for Numerical Methods, in ”Recent Advances in Numerical Analysis”, ed. C. de Boor and G. Golub (1978). · Zbl 0457.65049
[8] F. F. Gantmacher,The Theory of Matrices, vol. 2, Chelsea Publ. Co. N.Y. (1959). · Zbl 0085.01001
[9] H. O. Kreiss,Difference Methods for Stiff Ordinary Differential Equations, SIAM J. Numer. Anal. 15 (1978), 21–58. · Zbl 0385.65035
[10] O. Nevanlinna,On Error Bounds for G-stable Methods, BIT 16 (1976), 79–84. · Zbl 0321.65044
[11] O. Nevanlinna,On the Numerical Integration of Non-linear Initial Value Problems by Linear Multistep Methods, BIT 17 (1977), 58–71. · Zbl 0361.65063
[12] O. Nevanlinna and W. Liniger,Contractive Methods for Stiff Differential Equations, submitted to BIT (1978). · Zbl 0408.65045
[13] F. Odeh and W. Liniger,Non-linear Fixed-h Stability of Linear Multistep Formulas, J. Math. Anal. Applic. 61 (1977), 691–712. · Zbl 0378.65041
[14] O. Taussky,Matrices C with C n 0, Journal of Algebra 1 (1964), 5–10. · Zbl 0126.02802
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