Xiong You

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a r t i c l e i n f o a b s t r a c t For the perturbed oscillators in one-dimensional case, J.M. Franco designed the so-called Adapted Runge– Kutta–Nyström (ARKN) methods and derived the sufficient order conditions as well as the necessary and sufficient order conditions for ARKN methods based on the B-series theory [J.M. Franco, Runge–Kutta– Nyström(More)
Classical Runge-Kutta-Nyström (RKN) methods for second-order ordinary differential equations are extended to two-derivative Runge-Kutta-Nyström (TDRKN) methods involving the third derivative of the solution. A new version of Nyström tree theory and the corresponding B-series theory are developed, based on which the order conditions for TDRKN methods are(More)