In this paper, the method is evaluated using comparisons with full core Monte Carlo reference solutions of benchmark problems based on gas-cooled, graphite-moderated reactor core designs. Solutions are given for core eigenvalue problems and the calculation of fuel pin fission densities throughout the core. Using a single processor, results are found in minutes for small cores, and in no more than a few hours for a realistically large core; attempts to optimize the computational speed by parallel computing or advanced acceleration schemes are left for future work. Typical eigenvalues calculated by the method differ from reference solutions by less than 0.1 % , and pin fission density calculations have average accuracy of well within 1 % , even for unrealistically challenging core configuration problems. This new method enables the accurate determination of core eigenvalues and flux shapes in hexagonal cores with efficiency far exceeding that of other transport methods.