In recent years several numerical methods have been developed to integrate matrix differential systems whose solutions remain on a certain Lie group throughout the evolution. In this paper we describe some numerical methods derived for the solution of dynamical systems in the Lorentz quadratic group. This group has been extensively studied in past expecially by physiscists since some differential systems of great importance in relativity evolve in this group. Numerical tests will show the performance of the numerical methods described.
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