C¹-continuous time integration based on cubic Hermite interpolation

We discuss a C¹-continuous time integration method based on piecewise cubic Hermite approximation. This method, denoted as p2-scheme, belongs to a class of one-step integration methods derived recently [1]. It exhibits a convergence rate of order four and shows properties similar to variational integrators, such as an excellent long-term energy preservation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)