  In this work, we explore various relevant aspects of the Smoothed Particle
Hydrodynamics regarding Burger's equation. The stability, precision, and
efficiency of the algorithm are investigated in terms of different
implementations. In particular, we argue that the boundary condition plays an
essential role in the stability of numerical implementation. Besides, the issue
is shown to be closely associated with the initial particle distribution and
the interpolation scheme. Among others, we introduce an interpolation scheme
termed symmetrized finite particle method. The main advantage of the scheme is
that its implementation does not involve any derivative of the kernel function.
Concerning the equation of motion, the calculations are carried out using two
distinct scenarios where the particles are chosen to be either stationary or
dynamically evolved. The obtained results are compared with those obtained by
using the standard finite difference method for spatial derivatives. Our
numerical results indicate subtle differences between different schemes
regarding the choice of boundary condition. In particular, a novel type of
instability is observed where the regular distribution is compromised as the
particles start to traverse each other. Implications and further discussions of
the present study are also addressed.

Computational Physics