Frequency domain analysis of time integration algorithms (Q5946842)

The discrete generalized Bode's theorem is applied to the transfer functions of time integration algorithms for semi-discrete finite element equations. An integral equation is satisfied by discrete-time transfer functions of time integration algorithms. A characteristic of the spectral radius of the amplification matrix is derived to quantify the asymptotic mode annihilation capability of the algorithms. Numerical examples are presented to demonstrate the role of the characteristic gain.