Abstract
A necessary condition forB-stability is derived. Then it is shown that the Runge-Kutta methods of Lobatto type III A and III B and some other methods are notB-stable.
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J. C. Butcher,A stability property of implicit Runge-Kutta methods, BIT 15 (1975), 358–361.
B. L. Ehle,High order A-stable methods for the numerical solution of systems of D.E.'s, BIT 8 (1968), 276–278.
B. L. Ehle,On Padé approximations to the exponential function and A-stable methods for the numerical solution of initial value problems, Thesis, Univ. of Waterloo 1969.
R. Scherer,A note on Radau and Lobatto formulae for O.D.E.'s, BIT 17 (1977), 235–238.
H. J. Stetter,Analysis of discretization methods for ordinary differential equations, Berlin, Heidelberg, New York, Springer 1973.
G. Wanner,A short proof on nonlinear A-stability, BIT 16 (1976), 226–227.
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Scherer, R. A necessary condition forB-stability. BIT 19, 111–115 (1979). https://doi.org/10.1007/BF01931228
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DOI: https://doi.org/10.1007/BF01931228