Integral formulation and numerical simulations for the neutron transport equation in X-Y geometry

In this work the Nyström method was used to solve the integral formulation of the neutron transport equation in X-Y geometry. Four quadrature schemes were tested, namely, Gauss-Legendre, Gauss-Lobatto, Simpson, and Boole rules, for the numerical calculation of the integral formulation. Analytical techniques were used to remove singularities in order to accelerate the calculation scheme and to improve numerical accuracy. Explicit expressions were derived for evaluating relevant kernels. In addition to derive solutions for both fixed source and eigenvalue problems, the procedure provides pointwise solutions where ray effects are mitigated leading to numerical results with high order accuracy for two dimensional scalar flux. Numerical results are listed with up to seven correct significant digits.