In dispersed gas-liquid flows, the bubble size distribution plays an important role in the phase structure and interphase forces, which, in turn, determine the multiphase hydrodynamic behaviors, including the spatial profiles of the gas fraction, gas and liquid velocities, and mixing and mass-transfer behaviors. Thus, fluid particle coalescence and breakage phenomena are important for optimal operation of many industrial process units like the bubble column reactors. The population balance equation (PBE) is considered a concept for describing the evolution of populations of countable entities such as the bubbles in the bubble column. In recent studies, the least-squares method has been adopted for the solution of population balance (PB) problems. A favorable property of the weighted residual methods such as the least-squares technique is that the solution of the density function itself can be obtained from the fundamental PBE formulation, that is, not moment formulations. Hence, in this framework, the inner coordinate space is resolved. Although the interest in the least-squares method is a consequence of some favorable properties, the method should be compared to other techniques in the weighted residual family for the solution of integro-differential equations such as the PBE. For this reason, in this study, the performance of the least-squares method is compared to the orthogonal collocation, Galerkin and tau methods for the solutions of a PB problem describing bubbly flows. On the basis of the present PB model and simulation results, the simple orthogonal collocation method is considered a good candidate. The orthogonal collocation method holds the simplest algebra and, further, is computationally efficient and gives accurate solutions. In particular, the least-squares method suffers from relatively higher numerical error.