Block boundary value methods for linear Hamiltonian systems (Q1354253)

The article continues the work of the authors on boundary value methods for the numerical integration of ordinary differential equations. Here they study the application of these methods to the symplectic integration of linear Hamiltonian systems. Compared with the standard approach to linear multistep methods [see e.g. \textit{T. Eirola} and \textit{J. M. Sanz-Serna}, Numer. Math. 61, No. 3, 281-290 (1992; Zbl 0741.65056)] they find larger stability regions. Three families of methods are presented; two based on the trapezoidal rule and one achieving the maximum order \(p=2k\) for a \(k\)-step linear multistep method. As a numerical example the harmonic oscillator is treated.