×
Dahlquist, Germund

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

BIT, Nord. Tidskr. Inf.-behandl. 18, 384-401 (1978).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0413.65057

Cited in 3 Reviews
Cited in 106 Documents

MSC:

65L07 Numerical investigation of stability of solutions to ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations

Keywords:

G-stability; A-stability; accumulated error estimates; non-linear stiff problems; ordinary differential equations; multistep methods; numerical solution
PDF BibTeX XML Cite
\textit{G. Dahlquist}, BIT, Nord. Tidskr. Inf.-behandl. 18, 384--401 (1978; Zbl 0413.65057)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.