Continuous extensions to Nyström methods for second order initial value problems (Q1914870)

The aim of this article is to extend results on continuous, explicit Runge-Kutta methods by \textit{B. Owren} [Ph.D. thesis, Norwegian Institute of Technology, Trondheim, 1989] to explicit Nyström methods for second-order ordinary differential equations \(y''= f(x, y, y')\). After recalling some classical results, the order conditions of continuous Nyström methods (i.e., methods providing a dense output) are discussed. The main contribution consists in a detailed study of the maximum order attainable with an \(s\)-stage, continuous Nyström method.