Ion Accoustic Wave (IAW) dynamics are usually simulated assuming an isothermal Boltzmann fluid response of the electrons. It has been shown that results from the Boltzmann model may significantly differ from cor- responding ones obtained considering the fully kinetic electron dynamics, in particular wrt. the non-linear instability mechanisms of finite amplitude IAWs [1]. For ZTe /Ti 10 (Z the ionization degree and Te/i the electron/ion temperature), the positive contribution from trapped electrons to the non- linear kinetic frequency shift of IAWs in fact dominates over the negative one from trapped ions [2]. But carrying out simulations over IAW time scales while evolving fully kinetic electrons is a multi-scale computation and thus numerically very costly. For a spatially one-dimensional system, we shall present the implementation of an improved reduced electron model, the so- called adiabatic model, based on the adiabatic invariance of the phase space action u dx, [(x, u) the electron (position, velocity) in the wave frame, the integral being taken over a transit/bounce period for passing/trapped parti- cles] [3]. Simulations obtained with this adiabatic model, which only need to resolve the slow IAW time scale, are successfully compared to fully kinetic ones, in particular for computing non-linear frequency shifts of IAWs over different ZTe /Ti regimes resulting from both electron and ion trapping. [1] C. Riconda, A. Heron, D. Pesme, S. H¨ller, V. T. Tikhonchuk, and F. Detering, Phys. Rev. Lett. 94, 055003 (2005). [2] R. Berger, S. Brunner, T. Chapmann, L. Divol, C. H. Still, and E. J. Valeo, Phys. Plasmas 20, 032107 (2013). [3] R. L. Dewar, Phys. Fluids 15, 712 (1972).