Based on the Chebyshev collocation spectral method and Schur decomposition

two direct solvers for radiative discrete ordinates equations for a three-dimensional rectangular furnace with absorbing-emitting medium are developed.For the three-dimensional matrix equation from discretization of the radiative transfer equation

one solver is based on two-dimensional Schur decomposition after the transform of three-dimensional matrix equation to two-dimensional one using tensor product

and the other is based on three-dimensional Schur decomposition

which is developed in the present work.With the same parameters

the numerical experiments indicate that the new solvers can provide good accuracy.Compared with the standard discrete ordinates method

the new solvers are much faster

leading to less CPU time.Specially

the CPU time of the new solver based on the three-dimensional Schur decomposition is just 10%—1% of the standard discrete ordinates method.