Predictor-Corrector Methods for Periodic Second-Order Initial-Value Problems

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Abstract
Predictor-corrector methods are constructed for the accurate representation of the eigenmodes in the solution of second-order differential equations without first derivatives. These methods have (algebraic) order 4 and 6, and phase errors of orders up to 10. For linear and weakly nonlinear problems where homogeneous solution components dominate, the methods proposed in this paper are considerably more accurate than conventional methods.

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