A method of real-time dynamical simulation for laser interferometric gravitational wave detectors is presented. The method is based on a digital filtering approach and a number of important physical points understood by a step-by-step investigation of two-mirror cavities, a three-mirror coupled cavity, and a full-length power-recycled interferometer with mirrors having longitudinal motion. The final analytical representation used for the fast simulation of a full-length power-recycled interferometer is analogous to a two-mirror dynamical cavity with time-dependent reflectivities, when intracavity fields of the interferometer are expressed together in a state-vector representation. A detailed discussion establishes the relationships among physical effects pertaining to field evolution in two-mirror cavities and coupled cavities or to the full interferometer
