The Cayley transform in the numerical solution of unitary differential systems

In recent years some numerical methods have been developed to integrate matrix differential systems whose solutions are unitary matrices. In this paper we propose a new approach that transforms the original problem into a skew-Hermitian differential system by means of the Cayley transform. The new methods are semi-explicit, that is, no iteration is required but the solution of a certain number of linear matrix systems at each step is needed. Several numerical comparisons with known unitary integrators are reported.