Multi-step numerical integrators for time-dependent vibrating systems (Q1094929)

By means of the weighted residual method a general form of linear multistep methods is developed for time-dependent vibrating systems and a feasible two-step method is then obtained. Finally two examples are analyzed to show its applications to the initial value problems of time- dependent systems and the steady-state solution of periodically time- dependent ones. To the authors' knowledge, this is the first time that numerical methods for direct integration of the motion equations of time- dependent vibrating systems have been deeply investigated.