The Cayley Transform in the Numerical Solution of Unitary Differential Systems

n 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.