Abstract: A system for simulating an operation of a gas turbine engine is disclosed, having a computing system and a FADEC in electronic communication therewith, the computer system simulating an engine state. In each delta time, being the FADEC sampling rate (1) the FADEC: senses the simulated engine state from the computing system; determines a difference between the sensed state and a predetermined engine state; and outputs engine control commands intended for achieving the predetermined state; and (2) the computing system: receives the FADEC output; utilizes the output in an m×m Jacobian Block, having m active balances; and performs a reduced balance simulation, wherein: fewer than m columns of the Block are analyzed, the analysis of each column defining a Rolling Jacobian Pass; output from the Rolling Jacobian Passes is integrated into the Block, to define an updated simulated engine state; and the updated state is communicated to the FADEC.