An analysis of an unconditionally stable explicit method

Abstract Recently, several semi-implicit methods have been proposed for the time integration of the structural dynamics equations which are unconditionally stable yet explicit in their algorithmic structure. While these methods seem to violate the basic premise of the Courant requirement that the speed of information flow in the discrete model must not exceed that in the continuous problem, it is here shown that this is not the case. However, an analysis of the phase velocities of waves shows that the real flow of information of short wavelengths barely exceeds one spatial mesh per time step in these methods. Thus these semi-implicit methods appear to be useful primarily for problems dominated by very low frequencies, which is borne out by some estimates of computational costs made here.