Block boundary value methods for linear Hamiltonian systems

The problem of characterizing multistep methods suitable to efficiently approximate the solutions of linear Hamiltonian systems is discussed, showing that the appropriate methods should belong to the class of discrete Boundary Value Methods (BVMs). Three families of such methods are proposed. The presented methods have infinite regions of Absolute stability and can be of any order. In fact, for every odd k there are k-step methods of order up to 2k, which is the maximum order reachable by a Ic-step formula. (C) Elsevier Science Inc., 1997