CHEBYSHEV SERIES SOLUTION FOR RADIATIVE TRANSPORT IN A MEDIUM WITH A LINEARLY ANISOTROPIC SCATTERING PHASE FUNCTION

One-dimensional radiative heat transfer is considered in a plane-paral lel geometry for an absorbing, emitting, and linearly anisotropic scat tering medium subjected to azimuthally symmetric incident radiation at the boundaries. The integral form of the transport equation is used t hroughout the analysis. This formulation leads to a system of weakly-s ingular Fredholm integral equations of the second kind. The resulting unknown functions are then formally expanded in Chebyshev series. Thes e series representations are truncated at a specified number of terms, leaving residual functions as a result of the approximation. The coll ocation and the Ritz-Galerkin methods are formulated, and are expresse d in terms of general orthogonality conditions applied to the residual functions. The major contribution of the present work lies in develop ing quantitative error estimates, Error bounds are obtained for the ap proximating functions by developing equations relating the residuals t o the errors and applying functional norms to the resulting set of equ ations. The collocation and Ritz-Galerkin methods are each applied in turn to determine the expansion coefficients of the approximating func tions. The effectiveness of each method is interpreted by analyzing th e errors which result from the approximations.