Nystro¨m method applied to integral formulation of the neutron transport equation in X-Y geometry

Neutron transport problems in X-Y geometry have been solved with several techniques in last decades but it is still a challenge to produce a good balance between computational efficiency and accuracy. In this work, we address this problem by efficiently applying the Nystr¨om method to the integral formulation of the transport equation. Analytical techniques, modern numerical packages and optimized implementation were applied to reduce the computational time. This method presented results free of ray effects leading to high accurate numerical results for two-dimensional scalar flux. Our implementation simulates homogeneous problems with vacuum and reflective boundary conditions. Results were validated with up to seven significant digits and compared with those available in the literature. (author)