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Mathematics of Computation

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A nonexistence theorem for explicit $ A$-stable methods

Authors: Olavi Nevanlinna and Aarne H. Sipilä
Journal: Math. Comp. 28 (1974), 1053-1056
MSC: Primary 65L05
MathSciNet review: 0349021
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Abstract: It is proved that there are no A-stable explicit methods in a general class of "linear" methods. The class contains, for example, Runge-Kutta methods, linear multistep methods, predictor-corrector formulas, cyclic multistep methods and linear multistep methods with higher derivatives.

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  • [1] G. DAHLQUIST, "A special stability problem for linear multistep methods," Nordisk Tidskr. Informationsbehandling (BIT), v. 3, 1963, pp. 27-43. MR 30 #715. MR 0170477 (30:715)
  • [2] H. J. STETTER, Analysis of Discretization Methods for Ordinary Differential Equations, Springer, Berlin, 1973. MR 0426438 (54:14381)
  • [3] O. B. WIDLUND, "A note on unconditionally stable linear multistep methods," Nordisk Tidskr. Informationsbehandling (BIT), v. 7, 1967, pp. 65-70. MR 35 #6373. MR 0215533 (35:6373)

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Article copyright: © Copyright 1974 American Mathematical Society

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