Molecular Dynamic (MD) simulations have been conducted to look at the melting and solidification of the Lennard-Jones argon (100) interface with small amounts (up to 6.0K) of undercooling and superheating. By combining the fully equilibrated bulk phases of liquid and solid in one simulation box and counting the number of solid-like particles, the interface velocities, i.e. the growth rate or melting rate, were obtained as a function of temperature. The melting temperature, where no growth or melting of crystal particle is expected, is $T^*_m$=0.668 which is close to that of the Gibbs free energy calculation. A linear dependence of growth or melting rate on temperature was found except for high superheating, ${Delta}T$ > 6K. The high superheating is believed as the main source of slope discontinuity in the rate, not the misuse of initial regime as discussed in the earlier works.