Unitary integrators and applications to continuous orthonormalization techniques
SIAM Journal on Numerical Analysis
Runge-Kutta methods for orthogonal and isospectral flows
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Runge-Kutta type methods for orthogonal integration
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
SIAM Review
Applied Numerical Mathematics
Collocation and Relaxed Collocation for the Fer and the Magnus Expansions
SIAM Journal on Numerical Analysis
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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.