Discrete ordinates methods for neutral particle transport introduce ray effects, numerical artifacts arising from the discretization of the angular variable. Integral transport methods avoid this by eliminating angular variables entirely through integration over the solid angle. This project develops a Nyström-based approach to estimate scalar flux in two-dimensional fixed-source neutron transport problems in heterogeneous media, with isotropic scattering and vacuum and reflective boundary conditions. By working directly with the integral form of the transport equation, the method sidesteps ray effects while maintaining accuracy in geometrically complex configurations.