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)
Explicit trigonometrically fitted two-derivative Runge-Kutta (TFTDRK) methods solving second-order differential equations with oscillatory solutions are constructed. When the second derivative is available, TDRK methods can attain one algebraic order higher than Runge-Kutta methods of the same number of stages. TFTDRK methods have the favorable feature that(More)
This paper proposes and investigates the multidimensional extended Runge-Kutta-Nyström (ERKN) methods for the general second-order oscillatory system y″ + My = f(y, y′) where M is a positive semi-definite matrix containing implicitly the frequencies of the problem. The work forms a natural generalization of our previous work on ERKN methods for the special(More)