A comprehensive unified set of single-step algorithms with controllable dissipation for dynamics Part II. Algorithms and analysis Original Research Article

In Part I, a comprehensive unified set of single-step algorithms with controllable dissipation based on the generalized Galerkin formulation was presented. In this paper, the details of four lower-order algorithms using parametrized temporal finite element are presented. The analyses of the numerical stability, dissipation and dispersion are also provided. In comparison with the established algorithms, the present algorithms facilitate controllable dissipation and yield results of higher-order accuracy. Examples are also included to illustrate the validity of the algorithms.