A Fortran90 routine for the solution of orthogonal differential problems

In this paper we describe a Fortran90 routine for the numerical integration of orthogonal differential systems based on the Cayley transform methods. Three different implementations of the methods are given: with restart, with restart at each step and in composed form. Numerical tests will show the performances of the solver for the solution of orthogonal test problems, of orthogonal rectangular problems and for the calculation of Lyapunov exponents in the linear and nonlinear cases, and finally for solving inverse eigenvalue problem for Toeplitz matrices. The results obtained using Cayley methods are compared with those given by Fortran90 version of Munthe-Kaas methods, which have been coded in a similar way.