Short characteristic solution of the non-LTE line transfer problem by operator perturbation—II. The two-dimensional planar slab

Abstract We present the formal solution of the transfer problem in terms of the exponential short characteristic method and derive approximate operators that allow for the iterative solution of the non-LTE two-level atom problem. An eigenvalue analysis for the convergence rate of these operators and several approximate operators proposed by other authors is presented. The family of operators presented for the short characteristic approach range from local diagonal approximations to tridiagonal and pentadiagonal operators. The extension to multidimensions of the several proposed approximate operators is discussed.