Complete characterization of multistep methods with an interval of periodicity for solving $y^{\prime \prime }=f(x, y)$
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- by Rolf Jeltsch PDF
- Math. Comp. 32 (1978), 1108-1114 Request permission
Abstract:
Linear multistep methods for the second order differential equation $y” = - {\lambda ^2}y$, $\lambda$ real, are said to have an interval of periodicity if for a fixed $\lambda$ and a stepsize sufficiently small the numerical solution neither explodes nor decays. We give a very simple necessary and sufficient condition under which a linear multistep method has an interval of periodicity. This condition is then applied to multistep methods with an optimal error order.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 1108-1114
- MSC: Primary 65L05
- DOI: https://doi.org/10.1090/S0025-5718-1978-0501999-1
- MathSciNet review: 501999