Temporal discretization is a key aspect of the weakly compressible Smoothed Particle Hydrodynamics (SPH) method, as existing studies prove that the time integration schemes affect the stability of the simulations of weakly compressible SPH . In this study, accuracy and performance of the classical 4th order Runge-Kutta method as a time integration scheme was evaluated by comparing simulation results of 2D dam break problem in terms of pressure and free surface profiles with single step (Euler method), predictor-corrector (midpoint) schemes and existing simulation results given in the literature. Density correction algorithm was utilized as a baseline treatment to prevent density fluctuations. The effect of Artificial Particle Displacement (APD) algorithm is another numerical treatment which is investigated in the present work. It is observed that APD provides more homogeneous particle distribution, leading to a higher accuracy. As for the comparison between time integration schemes, results based on the free surface deformation indicate that the Runge-Kutta method achieves success at reducing the free surface particle scattering encountered on Euler and midpoint schemes.