The smoothed particle hydrodynamics (SPH) method is applied to construct the dispersion of fluctuations in quasi-hydrostatic configuration of an isothermal self-gravitating slab. The uncertainty of the implementation is evaluated, and a novel technique (acceleration error) is proposed to weaken this uncertainty. The two-fluid quasi-hydrostatic diffusion of small fluctuations is used to support the importance of the acceleration error. The results show that the uncertainty converges to a few percent by increasing of the SPH particle numbers. Considering the acceleration error weakens the uncertainty, and prohibits the serious dynamical consequences in slow dispersion of fluctuation in the quasi-hydrostatic evolution of the slab.