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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] Germund G. Dahlquist, A special stability problem for linear multistep methods, Nordisk Tidskr. Informations-Behandling 3 (1963), 27–43. MR 0170477
  • [2] Hans J. Stetter, Analysis of discretization methods for ordinary differential equations, Springer-Verlag, New York-Heidelberg, 1973. Springer Tracts in Natural Philosophy, Vol. 23. MR 0426438
  • [3] Olof B. Widlund, A note on unconditionally stable linear multistep methods, Nordisk Tidskr. Informations-Behandling 7 (1967), 65–70. MR 0215533

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Article copyright: © Copyright 1974 American Mathematical Society

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