A simple and effective new family of time marching procedures for dynamics

In this work, a new family of time-marching procedures for dynamics is introduced. The proposed algorithm is based on displacements-velocities relations, requiring no computation of accelerations. Thus, not only it is a very simple technique, but also it is truly self-starting. Unconditionally stable implicit and conditionally stable explicit approaches are focused here, and optimized procedures are discussed for these analyses. The new technique is second-order accurate with controllable period elongation and algorithmic dissipation. Numerical results are presented, illustrating the good performance of the method. The new family is simple, efficient and highly accurate, resulting in a very effective time-marching technique.