SEVERAL SYMBOLIC AUGMENTED CHEBYSHEV EXPANSIONS FOR SOLVING EQUATION OF RADIATIVE-TRANSFER

Three expansion methods are described using Chebyshev polynomials of t he first kind for solving the integral form of the equation of radiati ve transfer in an isotropically scattering, absorbing, and emitting pl ane-parallel medium. With the aid of symbolic computation, the unknown expansion coefficients associated with this choice of basis functions are shown to permit analytic resolution. A unified and systematic sol ution treatment is offered using the projection methods of collocation , Ritz-Galerkin, and weighted-Galerkin. Numerical results a re present ed contrasting the th ree expansion methods and comparing them with ex isting benchmark results. New theoretical results are presented illust rating rigorous error bounds, residual characteristics, accuracy, and convergence rates. (C) 1995 Academic Press, Inc.