ABSTRACT: The transport equation has a wide range of applications, including neutron transport and heat transfer, among others. Due to its high number of dimensions in the phase space and its integro-differential structure, the numerical simulation of this equation tends to be difficult and with high computational complexity, necessitating efficient and low-cost computational methods. This dissertation advances the field by applying the Nyström method, combined with a singularity subtraction technique, to two-dimensional fixed-source neutron transport problems. Unlike previous studies, this work introduces novel analytical and computational strategies, including domain subregioning, the clipping distance technique, and the manipulation of the Bickley-Naylor function. Such techniques play a crucial role in optimizing computational processes by identifying and eliminating redundant or non-essential calculations, increasing accuracy and efficiency. The methodology demonstrates significant improvements in solving two-dimensional homogeneous and heterogeneous medium problems with isotropic scattering. By addressing several benchmark problems and showing the method’s potential for broader applications, this research contributes a valuable computational tool to transport theory, offering perspectives for dealing with more complex scenarios in the future.