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We present a unified analysis for a family of variational time discretizationmethods, including discontinuous Galerkin methods and continuousGalerkin-Petrov methods, applied to non-stiff initial value problems. Besidesthe well-definedness of the methods, the global error and superconvergenceproperties are analyzed under rather weak abstract assumptions which also allowconsiderations of a wide variety of quadrature formulas. Numerical experimentsillustrate and support the theoretical results.

Unified Analysis for Variational Time Discretizations of Higher Order and Higher Regularity Applied to Non-stiff ODEs