A nonexistence theorem for explicit $A$-stable methods
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- by Olavi Nevanlinna and Aarne H. Sipilä PDF
- Math. Comp. 28 (1974), 1053-1056 Request permission
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.References
- Germund G. Dahlquist, A special stability problem for linear multistep methods, Nordisk Tidskr. Informationsbehandling (BIT) 3 (1963), 27–43. MR 170477, DOI 10.1007/bf01963532
- Hans J. Stetter, Analysis of discretization methods for ordinary differential equations, Springer Tracts in Natural Philosophy, Vol. 23, Springer-Verlag, New York-Heidelberg, 1973. MR 0426438, DOI 10.1007/978-3-642-65471-8
- Olof B. Widlund, A note on unconditionally stable linear multistep methods, Nordisk Tidskr. Informationsbehandling (BIT) 7 (1967), 65–70. MR 215533, DOI 10.1007/bf01934126
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 1053-1056
- MSC: Primary 65L05
- DOI: https://doi.org/10.1090/S0025-5718-1974-0349021-0
- MathSciNet review: 0349021