Abstract
For the integration of multi-frequency second-order oscillatory systems of differential equations, multidimensional extended Runge–Kutta–Nyström (MERKN) methods with FSAL property are investigated. Order conditions are presented. Phase properties are analysed and nonlinear stability of MERKN methods is proved. New practical MERKN methods with optimized phase and dissipation properties and embedded pairs of multidimensional MERKN methods are constructed. Numerical experiments are reported to show the high efficiency and robustness of our new methods compared with several well-known methods in the scientific literature.
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