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All symmetric interpolatory block-implicit methods of order less than six are A-stable. (English) Zbl 0561.65053

A theorem of Grace-Szegö is applied to show the A-stability of all symmetric interpolatory block-implicit methods involving five or less vectors per block.
Reviewer: J.M.Sanz-Serna

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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References:

[1] S. P. Nørsett and G. Wanner,The real-pole sandwich for rational approximations and oscillation equations. BIT 19 (1979), 79–94. · Zbl 0413.65011 · doi:10.1007/BF01931224
[2] N. Obreschkoff,Verteilung und Berechnung der Nullstellen reeller Polynome. DVW Berlin 1963. · Zbl 0156.28202
[3] G. Wanner,Characterization of all A-stable methods of order 2m - 4. BIT 20 (1980), 367–374. · Zbl 0475.65043 · doi:10.1007/BF01932779
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