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The aim of this work is to propose and analyze a new high order discontinuous Galerkin finite element method for the time integration of a Cauchy problem for second order ordinary differential equations. These equations typically arise after space semi-discretization of second order hyperbolic-type differen- tial problems, e.g., wave, elastodynamics and acoustics equations. After introducing the new method, we analyze its well-posedness and prove a-priori error estimates in a suitable (mesh-dependent) norm. Numerical results are also presented to verify our theoretical estimates

A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics