The State-of-the-Art of the LTA_N Method in the Solution of the Transport Equation in a Slab

In this work we report the state-of-the-art of the LTA_N method, reporting the derivation of the LTA_N homogeneous and particular solution in a slab for large N (N < 650), as well its accelerated version, which reduces drastically the computational time. We also sketch the mathematical background for the error bound estimate and convergence analysis of the LTA_N method. Finally, we display numerical results and comments.