This paper presents an efficient numerical integration method for a volume dynamics model in gas turbine engine transient simulations. It is a modified implicit Euler method that allows a time increment that would not be stable with the explicit Euler method. The Jacobian matrix of a nonlinear engine model is evaluated along the steady state engine operation line and scheduled as a function of the corrected shaft speed in advance, eliminating the necessity of computing during the simulation. The proposed method was applied to transient simulations of a compressor rig test model composed of a compressor, a nozzle with variable geometry and a volume placed between them. The eigenvalues of the simplified volume dynamics were analytically derived. It is shown that they are functions of the characteristic time of the volume defined by mass present in the volume divided by mass flow rate flowing into and out of the volume and dimensionless influence coefficients of nearby components.