Continuous extensions to Nyström methods for second order initial value problems

@article{Marthinsen1996ContinuousET,
  title={Continuous extensions to Nystr{\"o}m methods for second order initial value problems},
  author={Arne Marthinsen},
  journal={BIT Numerical Mathematics},
  year={1996},
  volume={36},
  pages={309-332}
}
In this work we consider interpolants for Nyström methods, i.e., methods for solving second order initial value problems. We give a short introduction to the theory behind the discrete methods, and extend some of the work to continuous, explicit Nyström methods. Interpolants for continuous, explicit Runge-Kutta methods have been intensively studied by several authors, but there has not been much effort devoted to continuous Nyström methods. We therefore extend some of the work by Owren.