High-order implicit time integration scheme with controllable numerical dissipation based on mixed-order Padé expansions

A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount controlled by a user-specified value spectral radius ρ∞ in frequency limit. Using this parameter as weight factor, Padé expansion matrix exponential solution equation motion constructed mixing diagonal and sub-diagonal expansions. An efficient time-stepping designed where systems equations, similar complexity to standard Newmark method, are solved recursively. It shown that proposed achieves high-frequency dissipation, while minimizing low-frequency period errors. effectiveness provided control efficiency demonstrated examples. simple guideline choice controlling step size provided. source codes written MATLAB FORTRAN available download at: https://github.com/ChongminSong/HighOrderTimeIntegration.