Complete characterization of multistep methods with an interval of periodicity for solving
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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Keywords: Linear multistep methods, second order differential equations, orbital stability, interval of periodicity, optimal methods, growth parameters
Article copyright: © Copyright 1978 American Mathematical Society