In this article, we investigate the interaction of two identical discrete solitons (DSs) in a semi-infinite nonlinear waveguide array (WA). Under a continuous approximation, we develop a semi-analytical treatment based on the variational method to obtain a set of coupled ordinary differential equations that describe the interaction mechanism. Identical solitons without a phase difference are observed to exhibit an attractive potential. The results from the variational calculation obtained under continuous approximation show a strong agreement with the numerical results of DS interaction. We further investigate the role of the different soliton parameters on the collision point of two identical solitons on this potential and thus the location of the collision point as a result.