  In this work we investigate the use of the Analytical Discrete Ordinates
(ADO) method when solving the spectral approximation of the nonclassical
transport equation. The spectral approximation is a recently developed method
based on the representation of the nonclassical angular flux as a series of
Laguerre polynomials. This representation generates, as outcome, a system of
equations that have the form of classical transport equations and can therefore
be solved by current deterministic algorithms. Thus, the investigation of
efficient approaches to solve the nonclassical transport equation is of
interest and shall be pursued. This is the case of the ADO method which has
been successfully used to solve a wide class of problems in the general area of
particle transport. Numerical results are presented for two nonclassical test
problems in slab geometry. These nonclassical transport problems are chosen in
such way that their solution exactly reproduces the solution of the classical
diffusion problem. Very accurate results are obtained for both test problems.
However, the use of high precision arithmetic is sometimes required as
illustrated in the second test problem. Limitations of the spectral
approximation are also analyzed and discussed.
