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

摘要

Predictor-corrector methods for the accurate representation of the eigenmodes in the solution of second-order differential equations without first derivatives are constructed. The 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 are considerably more accurate than conventional methods.