The residual method of orthogonal collocations (OCs) is evaluated on the basis of  three problems of increasing degree of complexity. Two model problems, a Poisson equation and a wave front propagation problem, allow a comparison with known analytical solutions and other numerical results obtained with finite differences or with the classical Galerkin method. The third problem consists of the numerical solution of the equations describing a one-dimensional sodium vapor flow, obtained using a variant of the BL0W-3A computer program developed for this purpose. Shape functions of second degree are used throughout the analysis. The results show the applicability of the OC technique to two-phase flow problems.