Complete characterization of multistep methods with an interval of periodicity for solving
Math. Comp. 32 (1978), 1108-1114
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Abstract: Linear multistep methods for the second order differential equation , real, are said to have an interval of periodicity if for a fixed 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.
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Department of Mathematics, University of Kentucky, Lexington, Ky., 1976.
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Linear multistep methods,
second order differential equations,
interval of periodicity,
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American Mathematical Society