Numerical integration of a class of ordinary differential equation on the general linear group of matrices

This paper concerns with the numerical solution of a class of ordinary differential equations on Gl(n), the set of all n × n nonsingular real matrices. In particular, we consider matrix dynamical systems of the form Y^{\PRIME}= Y ^{−T}F(Y). The presence of the inverse of the solution and of possible escape times make the numerical solution of this kind of differential equations somewhat worrisome. Here, we suggest some numerical techniques to avoid some problems arising in its numerical solution.